| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To complete the square for the quadratic expression \(-20x^2 + 4x - 1\), follow these steps: 1. **Factor out the coefficient of \(x^2\) from the first two terms:** \[ -20x^2 + 4x - 1 = -20(x^2 - \frac{1}{5}x) - 1 \] 2. **Complete the square inside the parentheses:** - Take the coefficient of \(x\) inside the parentheses, which is \(-\frac{1}{5}\), divide it by 2, and square it: \[ \left(\frac{-\frac{1}{5}}{2}\right)^2 = \left(-\frac{1}{10}\right)^2 = \frac{1}{100} \] - Add and subtract this square inside the parentheses: \[ -20\left(x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100}\right) - 1 \] - This can be rewritten as: \[ -20\left((x - \frac{1}{10})^2 - \frac{1}{100}\right) - 1 \] 3. **Distribute the \(-20\) and simplify:** \[ -20(x - \frac{1}{10})^2 + 20 \cdot \frac{1}{100} - 1 \] \[ -20(x - \frac{1}{10})^2 + \frac{20}{100} - 1 \] \[ -20(x - \frac{1}{10})^2 + \frac{1}{5} - 1 \] \[ -20(x - \frac{1}{10})^2 - \frac{4}{5} \] Thus, the completed square form of the quadratic expression is: \[ \boxed{-20(x - \frac{1}{10})^2 - \frac{4}{5}} \] |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| deepseek-r1 | To complete the square for the quadratic \(-20x^2 + 4x - 1\), we start by factoring out the coefficient of \(x^2\) from the first two terms: \[ -20x^2 + 4x - 1 = -20\left(x^2 - \frac{1}{5}x\right) - 1 \] Next, we complete the square inside the parentheses. The coefficient of \(x\) is \(-\frac{1}{5}\). Half of this coefficient is \(-\frac{1}{10}\), and squaring it gives \(\left(-\frac{1}{10}\right)^2 = \frac{1}{100}\). We add and subtract this value inside the parentheses: \[ -20\left(x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100}\right) - 1 \] This can be rewritten as: \[ -20\left(\left(x - \frac{1}{10}\right)^2 - \frac{1}{100}\right) - 1 \] Distributing the \(-20\) across the terms inside the parentheses: \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{20}{100} - 1 \] Simplifying the constants: \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{1}{5} - 1 \] Combining the constants \(\frac{1}{5} - 1\) gives: \[ -20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5} \] Thus, the quadratic in completed square form is \(\boxed{-20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5}}\). |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| gpto1 | To complete the square for the quadratic \( -20x^2 + 4x - 1 \), follow these steps: 1. **Factor out the coefficient of \( x^2 \) from the first two terms:** \[ -20x^2 + 4x - 1 = -20\left( x^2 - \frac{4}{20}x \right) - 1 = -20\left( x^2 - \frac{1}{5}x \right) - 1 \] 2. **Complete the square inside the parentheses:** - Take half of the coefficient of \( x \): \[ \frac{-\frac{1}{5}}{2} = -\frac{1}{10} \] - Square this value and add and subtract inside the parentheses: \[ x^2 - \frac{1}{5}x = \left( x - \frac{1}{10} \right)^2 - \left( \frac{1}{10} \right)^2 \] - Rewrite the expression: \[ -20\left[ \left( x - \frac{1}{10} \right)^2 - \frac{1}{100} \right] - 1 \] 3. **Simplify the expression:** - Distribute \( -20 \): \[ -20\left( x - \frac{1}{10} \right)^2 + 20\left( \frac{1}{100} \right) - 1 = -20\left( x - \frac{1}{10} \right)^2 + \frac{1}{5} - 1 \] - Simplify constants: \[ \frac{1}{5} - 1 = -\frac{4}{5} \] - Final expression: \[ -20\left( x - \frac{1}{10} \right)^2 - \frac{4}{5} \] **Final Answer:** \(\boxed{\displaystyle -20\left( x-\dfrac{1}{10} \right)^2\,-\,\dfrac{4}{5}}\) |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| gpt-4o-2024-08-06 | To complete the square for the quadratic expression \(-20x^2 + 4x - 1\), we start by focusing on the quadratic and linear terms: \(-20x^2 + 4x\). First, factor out the coefficient of \(x^2\) from these terms: \[ -20x^2 + 4x = -20(x^2 - \frac{4}{20}x) = -20(x^2 - \frac{1}{5}x) \] Next, we complete the square inside the parentheses. To do this, take the coefficient of \(x\), which is \(-\frac{1}{5}\), divide it by 2, and square the result: \[ \left(-\frac{1}{5} \times \frac{1}{2}\right)^2 = \left(-\frac{1}{10}\right)^2 = \frac{1}{100} \] Add and subtract this square inside the parentheses: \[ x^2 - \frac{1}{5}x = \left(x^2 - \frac{1}{5}x + \frac{1}{100}\right) - \frac{1}{100} \] This can be rewritten as: \[ \left(x - \frac{1}{10}\right)^2 - \frac{1}{100} \] Now, substitute back into the expression with the factor of \(-20\): \[ -20\left(\left(x - \frac{1}{10}\right)^2 - \frac{1}{100}\right) \] Distribute the \(-20\): \[ -20\left(x - \frac{1}{10}\right)^2 + 20 \times \frac{1}{100} \] Simplify the constant term: \[ 20 \times \frac{1}{100} = \frac{20}{100} = \frac{1}{5} \] Now, include the constant term from the original expression, which is \(-1\): \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{1}{5} - 1 \] Combine the constant terms: \[ \frac{1}{5} - 1 = \frac{1}{5} - \frac{5}{5} = -\frac{4}{5} \] Thus, the expression in completed square form is: \[ -20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5} \] The final answer is: \[ \boxed{-20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5}} \] |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| DeepSeek-Coder-V2-Lite-Instruct | To complete the square for the quadratic expression \(-20 x^2 + 4 x - 1\), we will follow these steps: 1. **Factor out the coefficient of \(x^2\) from the first two terms:** \[ -20 x^2 + 4 x - 1 = -20 \left( x^2 - \frac{4}{20} x \right) - 1 \] Simplify the fraction: \[ -20 \left( x^2 - \frac{1}{5} x \right) - 1 \] 2. **Complete the square inside the parentheses:** To complete the square, we need to add and subtract the square of half the coefficient of \(x\): \[ x^2 - \frac{1}{5} x \] The coefficient of \(x\) is \(-\frac{1}{5}\), so half of this is \(-\frac{1}{10}\), and its square is \(\left( -\frac{1}{10} \right)^2 = \frac{1}{100}\). Add and subtract \(\frac{1}{100}\) inside the parentheses: \[ x^2 - \frac{1}{5} x + \frac{1}{100} - \frac{1}{100} \] This can be rewritten as: \[ \left( x - \frac{1}{10} \right)^2 - \frac{1}{100} \] 3. **Substitute back into the original expression:** \[ -20 \left( \left( x - \frac{1}{10} \right)^2 - \frac{1}{100} \right) - 1 \] Distribute the \(-20\): \[ -20 \left( x - \frac{1}{10} \right)^2 + \frac{20}{100} - 1 \] Simplify the fraction: \[ -20 \left( x - \frac{1}{10} \right)^2 + \frac{1}{5} - 1 \] Combine the constants: \[ -20 \left( x - \frac{1}{10} \right)^2 - \frac{4}{5} \] Thus, the completed square form of the quadratic expression \(-20 x^2 + 4 x - 1\) is: \[ \boxed{-20 \left( x - \frac{1}{10} \right)^2 - \frac{4}{5}} \] |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| Meta-Llama-3.1-405B-Instruct-Turbo | ## Step 1: Identify the coefficients of the quadratic equation The given quadratic equation is $-20x^2 + 4x - 1$. The coefficients are $a = -20$, $b = 4$, and $c = -1$. ## Step 2: Determine the number to complete the square To complete the square, we need to add and subtract $(\frac{b}{2})^2$ inside the parentheses. However, since the coefficient of $x^2$ is not 1, we need to factor it out first. The number to complete the square is $(\frac{b}{2a})^2$. ## Step 3: Calculate the number to complete the square We calculate $(\frac{b}{2a})^2 = (\frac{4}{2 \cdot -20})^2 = (\frac{4}{-40})^2 = (\frac{1}{-10})^2 = \frac{1}{100}$. ## Step 4: Rewrite the quadratic equation to complete the square We rewrite the quadratic equation as $-20(x^2 - \frac{1}{5}x) - 1$. ## Step 5: Add and subtract the number to complete the square We add and subtract $\frac{1}{100}$ inside the parentheses: $-20(x^2 - \frac{1}{5}x + \frac{1}{100}) - 1 + \frac{1}{5}$. ## Step 6: Factor the perfect square trinomial The expression inside the parentheses is now a perfect square trinomial: $-20(x - \frac{1}{10})^2 - 1 + \frac{1}{5}$. ## Step 7: Simplify the constant term We simplify the constant term: $-1 + \frac{1}{5} = -\frac{4}{5}$. ## Step 8: Write the final completed square form The final completed square form is $-20(x - \frac{1}{10})^2 - \frac{4}{5}$. The final answer is: $\boxed{-20(x - \frac{1}{10})^2 - \frac{4}{5}}$ |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| Meta-Llama-3.1-70B-Instruct-Turbo | ## Step 1: Identify the coefficients of the quadratic equation The given quadratic equation is $-20x^2 + 4x - 1$. The coefficients are $a = -20$, $b = 4$, and $c = -1$. ## Step 2: Determine the sign of the coefficient of $x^2$ Since $a = -20$ is negative, we need to factor out $-1$ from the quadratic and linear terms to make the coefficient of $x^2$ positive. ## Step 3: Factor out $-1$ from the quadratic and linear terms Factoring out $-1$ gives $-(20x^2 - 4x) - 1$. ## Step 4: Complete the square for the quadratic expression To complete the square for $20x^2 - 4x$, we need to add and subtract $(\frac{b}{2})^2$ inside the parentheses. Since $b = -4$, we have $(\frac{-4}{2})^2 = 4$. However, because we factored out $-1$, we actually need to add and subtract $-4$ inside the parentheses to maintain equivalence. ## Step 5: Add and subtract $-4$ inside the parentheses Adding and subtracting $-4$ gives $-(20x^2 - 4x + 4 - 4) - 1$. ## Step 6: Rewrite the expression with the completed square This can be rewritten as $-(20x^2 - 4x + 4) + 4 - 1$, which simplifies to $-(20x^2 - 4x + 4) + 3$. ## Step 7: Factor the perfect square trinomial The expression $20x^2 - 4x + 4$ can be factored as $20(x - \frac{1}{5})^2$ but since we are completing the square, we keep it in the form $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ and then simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is also not correct, the correct simplification is $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - 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\frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - 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\frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{10})^2$ is not correct, instead we simplify to $20(x^2 - \frac{1}{5}x + \frac{1}{25})$ is not correct, instead we simplify to $20(x - \frac{1}{5})^2$ is not correct, instead we simplify to $20(x^2 - \ |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| Qwen2-72B-Instruct | To complete the square for the quadratic expression \(-20x^2 + 4x - 1\), we follow these steps: 1. Factor out the coefficient of \(x^2\) from the first two terms. 2. Complete the square by adding and subtracting the square of half the coefficient of \(x\). 3. Simplify the expression. Let's go through these steps: ### Step 1: Factor out the coefficient of \(x^2\) \[ -20x^2 + 4x - 1 = -20(x^2 - \frac{1}{5}x) - 1 \] ### Step 2: Complete the square The coefficient of \(x\) inside the parentheses is \(-\frac{1}{5}\). Half of this coefficient is \(-\frac{1}{10}\), and its square is \(\left(-\frac{1}{10}\right)^2 = \frac{1}{100}\). Add and subtract \(\frac{1}{100}\) inside the parentheses, but remember to multiply it by the factor outside the parentheses (\(-20\)) when you add it outside to keep the equation balanced. \[ -20\left(x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100}\right) - 1 \] ### Step 3: Simplify the expression \[ -20\left[\left(x - \frac{1}{10}\right)^2 - \frac{1}{100}\right] - 1 \] Distribute the \(-20\) back into the expression: \[ -20\left(x - \frac{1}{10}\right)^2 + 20\cdot\frac{1}{100} - 1 \] Simplify: \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{1}{5} - 1 \] Combine constants: \[ -20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5} \] So, the completed square form of \(-20x^2 + 4x - 1\) is: \[ \boxed{-20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5}} \] |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| baichuan4 | To complete the square for the quadratic $-20x^2 + 4x - 1$, we first need to identify the coefficients of the quadratic terms and the linear term. The coefficient of the quadratic term is $-20$, and the coefficient of the linear term is $4$. Our goal is to rewrite the quadratic in the form $(ax + b)^2 + c$, where $a$, $b$, and $c$ are constants. To do this, we need to ensure that the coefficient of the $x^2$ term is $1$. We can achieve this by dividing the entire equation by the coefficient of the quadratic term, which is $-20$. However, to make the calculations simpler, we can first divide the equation by the absolute value of the coefficient, which is $20$, and then adjust the sign later. Dividing the equation by $20$, we get: $$ x^2 - \frac{4}{20}x + \frac{1}{20} $$ Simplifying the fraction, we have: $$ x^2 - \frac{1}{5}x + \frac{1}{20} $$ Now, we need to complete the square. To do this, we take half of the coefficient of the linear term, square it, and add it to both sides of the equation. The coefficient of the linear term is $-\frac{1}{5}$, so half of it is $-\frac{1}{10}$. Squaring this, we get $\left(-\frac{1}{10}\right)^2 = \frac{1}{100}$. Adding this to both sides of the equation, we get: $$ x^2 - \frac{1}{5}x + \frac{1}{100} = \frac{1}{20} + \frac{1}{100} $$ Simplifying the right-hand side, we have: $$ x^2 - \frac{1}{5}x + \frac{1}{100} =frac{5frac{5}{100} + \frac{1}{100} $$ x $$ x^2 - \frac{1}{5}x + \frac{1}{100} = \frac{6}{100} $$ $$ x^2 - \frac{1}{5}x + \frac{1}{100} = \frac{3}{50} $$ Now, we can rewrite the left-hand side as a perfect square: $$ \left(x - \frac{1}{10}\right)^2 = \frac{3}{50} $$ Finally, we need to adjust the sign of the equation to match the original equation. Since we initially divided the equation by $20$ instead of $-20$, we need to multiply both sides of the equation by $-1$ to get the correct sign: $$ -\left(x - \frac{1}{10}\right)^2 = -\frac{3}{50} $$ Simplifying the right-hand side, we have: $$ -\left(x - \frac{1}{10}\right)^2 = -\frac{6}{100} $$ $$ -\left(x - \frac{1}{10}\right)^2 = -\frac{3}{50} $$ Therefore, the completed square form of the quadratic $-20x^2 + 4x - 1$ is: $$ -\left(x - \frac{1}{10}\right)^2 - \frac{3}{50} $$ Putting the final answer in a box, we have: $$ \boxed{-\left(x - \frac{1}{10}\right)^2 - \frac{3}{50}} $$ |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| doubao | $-20x^2+4x-1$ $=-20(x^2-\frac{4}{20}x)-1$ $=-20(x^2-\frac{1}{5}x)-1$ $=-20(x^2-\frac{1}{5}x+\frac{1}{100}-\frac{1}{100})-1$ $=-20(x^2-\frac{1}{5}x+\frac{1}{100})+(-20)\times(-\frac{1}{100})-1$ $=-20(x-\frac{1}{10})^2+\frac{1}{5}-1$ $=-20(x-\frac{1}{10})^2-\frac{4}{5}$ $\\boxed{-20(x-\frac{1}{10})^2-\frac{4}{5}}$。 |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| gpto1 | To complete the square for the quadratic \( -20x^2 + 4x - 1 \), follow these steps: 1. **Factor out the coefficient of \( x^2 \) from the first two terms:** \[ -20x^2 + 4x - 1 = -20\left( x^2 - \frac{4}{20}x \right) - 1 = -20\left( x^2 - \frac{1}{5}x \right) - 1 \] 2. **Complete the square inside the parentheses:** - Take half of the coefficient of \( x \): \[ \frac{-\frac{1}{5}}{2} = -\frac{1}{10} \] - Square this value and add and subtract inside the parentheses: \[ x^2 - \frac{1}{5}x = \left( x - \frac{1}{10} \right)^2 - \left( \frac{1}{10} \right)^2 \] - Rewrite the expression: \[ -20\left[ \left( x - \frac{1}{10} \right)^2 - \frac{1}{100} \right] - 1 \] 3. **Simplify the expression:** - Distribute \( -20 \): \[ -20\left( x - \frac{1}{10} \right)^2 + 20\left( \frac{1}{100} \right) - 1 = -20\left( x - \frac{1}{10} \right)^2 + \frac{1}{5} - 1 \] - Simplify constants: \[ \frac{1}{5} - 1 = -\frac{4}{5} \] - Final expression: \[ -20\left( x - \frac{1}{10} \right)^2 - \frac{4}{5} \] **Final Answer:** \(\boxed{\displaystyle -20\left( x-\dfrac{1}{10} \right)^2\,-\,\dfrac{4}{5}}\) |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| kimi | To complete the square for the quadratic expression \(-20x^2 + 4x - 1\), we will follow these steps: 1. **Factor out the coefficient of \(x^2\) from the first two terms:** \[ -20x^2 + 4x - 1 = -20(x^2 - \frac{1}{5}x) - 1 \] 2. **Complete the square inside the parentheses:** To complete the square for \(x^2 - \frac{1}{5}x\), we need to add and subtract the square of half the coefficient of \(x\). The coefficient of \(x\) is \(-\frac{1}{5}\), so half of this is \(-\frac{1}{10}\), and squaring it gives \(\left(-\frac{1}{10}\right)^2 = \frac{1}{100}\). Adding and subtracting \(\frac{1}{100}\) inside the parentheses: \[ x^2 - \frac{1}{5}x = x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100} \] 3. **Rewrite the expression as a perfect square trinomial:** \[ x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100} = \left(x - \frac{1}{10}\right)^2 - \frac{1}{100} \] 4. **Substitute back into the original expression:** \[ -20\left(x^2 - \frac{1}{5}x\right) - 1 = -20\left(\left(x - \frac{1}{10}\right)^2 - \frac{1}{100}\right) - 1 \] 5. **Distribute the \(-20\):** \[ -20\left(x - \frac{1}{10}\right)^2 + 20 \cdot \frac{1}{100} - 1 \] Simplify \(20 \cdot \frac{1}{100}\): \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{1}{5} - 1 \] 6. **Combine the constant terms:** \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{1}{5} - \frac{5}{5} = -20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5} \] 7. **Write the final answer within a box:** \[ \boxed{-20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5}} \] |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| minimax | To complete the square for the quadratic equation $-20x^2 + 4x - 1$, we need to express it in the form of $(ax + b)^2 + c$. First, let's factor out the coefficient of $x^2$ from the first two terms: $$-20x^2 + 4x - 1 = -20(x^2 - \frac{4}{20}x) - 1$$ Simplify the fraction: $$-20(x^2 - \frac{1}{5}x) - 1$$ Now, we need to find a value to complete the square. This value is $(\frac{b}{2a})^2$, where $a$ is the coefficient of $x^2$ and $b$ is the coefficient of $x$ in the quadratic expression $ax^2 + bx + c$. In our case, $a = -20$ and $b = -1$ (after factoring out the -20 from the $x$ term), so: $$\left(\frac{-1}{2 \cdot -20}\right)^2 = \left(\frac{1}{40}\ |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| wenxinyiyan | 首先，我们需要将二次项的系数化为1，这样我们才能更容易地完成平方。我们可以通过除以-20来实现这一点： $-20x^2 + 4x - 1 = -20(x^2 - \frac{1}{5}x) - 1$ 然后，我们需要找到一个数，使得$x^2 - \frac{1}{5}x$可以变成一个完全平方。这个数应该是$\frac{1}{5}$的一半，即$\frac{1}{10}$，然后平方它，得到$\frac{1}{100}$。 接下来，我们将$\frac{1}{100}$加到$x^2 - \frac{1}{5}x$中，并同时从整个表达式中减去$\frac{1}{100}$以保持等式的平衡： $-20(x^2 - \frac{1}{5}x) - 1 = -20(x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100}) - 1$ 现在我们可以完成平方了： $-20(x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100}) - 1 = -20[(x - \frac{1}{10})^2 - \frac{1}{100}] - 1$ 最后，我们可以将-20分配到括号内的每一项，并将常数项合并： $-20[(x - \frac{1}{10})^2 - \frac{1}{100}] - 1 = -20(x - \frac{1}{10})^2 + \frac{1}{5} - 1 = \boxed{-20(x - \frac{1}{10})^2 - \frac{4}{5}}$ |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| zhipu | To complete the square for the quadratic $-20x^2 + 4x - 1$, follow these steps: 1. **Factor out the coefficient of $x^2$ from the first two terms:** \[ -20x^2 + 4x - 1 = -20(x^2 - \frac{4}{20}x) - 1 \] Simplify the fraction: \[ -20(x^2 - \frac{1}{5}x) - 1 \] 2. **Complete the square inside the parentheses:** - Take half of the coefficient of $x$, which is $-\frac{1}{5}$, and square it: \[ \left(-\frac{1}{5} \cdot \frac{1}{2}\right)^2 = \left(-\frac{1}{10}\right)^2 = \frac{1}{100} \] - Add and subtract this square inside the parentheses: \[ -20\left(x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100}\right) - 1 \] - Rearrange to form a perfect square trinomial: \[ -20\left(\left(x - \frac{1}{10}\right)^2 - \frac{1}{100}\right) - 1 \] 3. **Distribute the $-20$ and simplify:** \[ -20\left(x - \frac{1}{10}\right)^2 + 20\cdot\frac{1}{100} - 1 \] \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{20}{100} - 1 \] \[ -20\left(x - \frac{1}{10}\right)^2 + \frac{1}{5} - 1 \] Convert $\frac{1}{5}$ to a common denominator with $-1$: \[ \frac{1}{5} - 1 = \frac{1}{5} - \frac{5}{5} = -\frac{4}{5} \] Thus, the completed square form of the quadratic $-20x^2 + 4x - 1$ is: \[ \boxed{-20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5}} \] |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |
| deepseek-v3 | To complete the square for the quadratic expression \(-20x^2 + 4x - 1\), follow these steps: ### Step 1: Factor out the coefficient of \(x^2\) from the first two terms \[ -20x^2 + 4x - 1 = -20(x^2 - \frac{1}{5}x) - 1 \] ### Step 2: Complete the square inside the parentheses Take half of the coefficient of \(x\), square it, and add and subtract this value inside the parentheses: \[ x^2 - \frac{1}{5}x \quad \text{(Coefficient of \(x\) is \(-\frac{1}{5}\))} \] \[ \left(-\frac{1}{5} \times \frac{1}{2}\right)^2 = \left(-\frac{1}{10}\right)^2 = \frac{1}{100} \] \[ x^2 - \frac{1}{5}x + \frac{1}{100} - \frac{1}{100} = \left(x - \frac{1}{10}\right)^2 - \frac{1}{100} \] ### Step 3: Substitute back into the expression \[ -20\left(\left(x - \frac{1}{10}\right)^2 - \frac{1}{100}\right) - 1 \] \[ = -20\left(x - \frac{1}{10}\right)^2 + \frac{20}{100} - 1 \] \[ = -20\left(x - \frac{1}{10}\right)^2 + \frac{1}{5} - 1 \] \[ = -20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5} \] ### Final Answer \[ \boxed{-20\left(x - \frac{1}{10}\right)^2 - \frac{4}{5}} \] |
-20 \left(x-\frac{1}{10}\right)^2-\frac{4}{5} |