Question

What is the intermediate step in the form (x + a)2 = b as a result of

completing the square for the following equation?
-3x2 - 36x = 300

Answer 1

we need to add a²=6² to both sides of
`x^2+12x+6^2=-100+6^2` in order to rewrite in the form
`\left(x\:+\:a\right)^2\:=\:b`.

Explanation:

Given the equation

`-3x^2-36x=300`

First of all, we need to divide both sides by -3 to simplify it

i.e.

`(-3x^2-36x)/(-3)=(300)/(-3)`

`x^2+12x=-100`

In order to rewrite in the form
`\left(x\:+\:a\right)^2\:=\:b`, we need to add a²=6² to both sides

`x^2+12x+6^2=-100+6^2`

so

`\left(x+6\right)^2=-64`

Therefore, we need to add a²=6² to both sides of
`x^2+12x+6^2=-100+6^2` in order to rewrite in the form
`\left(x\:+\:a\right)^2\:=\:b`.