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} (-5x^2)/(-5)+(-90x)/(-5)=(-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+((18)/(2))^2=111+((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`