Question

What is the intermediate step in the form (x+a)^2 =b as a result of completing the square for the following equation?

Answer 1

Given the equation:

$-5x^2-90x=-555$

We will make a complete square to write the equation as the form (x+a)² = b

So, the steps will be as follows:

1) divide the equation by (-5) to make the coefficient of x²=1

$\begin{gathered} \frac{-5x^2}{-5}+\frac{-90x}{-5}=\frac{-555}{-5} \\ \\ x^2+18x=111 \end{gathered}$

2) we will add a number = (18/2)² to both sides to complete the square

so,

$\begin{gathered} x^2+18x+(\frac{18}{2})^2=111+(\frac{18}{2})^2 \\ x^2+18x+81=111+81 \\ \\ x^2+18x+81=192 \end{gathered}$

3) factor the left-side

$(x+9)^2=192$

So, the answer will be:

$(x+9)^2=192$