#4 ### Completing the Square to Solve an Equation#### Fill in the blank so that the resulting statement is true:To solve \( x^2 - \frac{4}{11}x = \frac{16}{121} \) by completing the square, add [blank] to both sides of the equation.(Type an integer or a simplified fraction.)In order to complete the square for the equation \( x^2 - \frac{4}{11}x = \frac{16}{121} \), we need to find a value that makes the left-hand side of the equation a perfect square trinomial.1. Take the coefficient of \( x \), which is \( -\frac{4}{11} \).2. Divide it by 2: \[ -\frac{4}{11} \div 2 = -\frac{2}{11} \]3. Square the result: \[ \left(-\frac{2}{11}\right)^2 = \frac{4}{121} \]So, we need to add \( \frac{4}{121} \) to both sides of the equation.Therefore, the blank should be filled with:\[ \boxed{\frac{4}{121}} \]By adding \( \frac{4}{121} \) to both sides, the equation becomes:\[ x^2 - \frac{4}{11}x + \frac{4}{121} = \frac{16}{121} + \frac{4}{121} \]\[ \left( x - \frac{2}{11} \right)^2 = \frac{20}{121} \]This completes the square and simplifies solving the equation.

Name: #4 ### Completing the Square to Solve an Equation#### Fill in the blan
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: #4 ### Completing the Square to Solve an Equation#### Fill in the blank so that the resulting statement is true:To solve \( x^2 - \frac{4}{11}x = \frac{16}{121} \) by completing the square, add [blank] to both sides of the equation.(Type an integer o