Question

question
if using the method of completing the square to solve the quadratic equation below, which number would have to be added to \complete the square\?

$x^{2}-13x = 11$

Explanation:

Step1: Recall the formula for completing the square

For the quadratic expression $x^{2}+bx$, the number to add to complete the square is $(\frac{b}{2})^{2}$.

Step2: Identify the value of $b$

In the equation $x^{2}-13x = 11$, the coefficient of $x$ is $b=- 13$.

Step3: Calculate the number to add

Substitute $b = - 13$ into $(\frac{b}{2})^{2}$. We get $(\frac{-13}{2})^{2}=\frac{169}{4}$.

Answer:

$\frac{169}{4}$