Question

How do you solve `5x^2 + 20x - 120 = 0` using completing the square?

Answer 1

Logical first step would be to divide everything by `5`

Explanation:

`->x^2+4x-24=0`

Since `(x+a)^2=x^2 +2ax+a^2`
We take half of the coefficient of `x`, and square it:
`x^2+4x+4=(x+2)^2`

We have to balance the `4` we used with the `-24`
So the equation becomes:
`x^2+4x+4-28=0->` add 28:
`(x+2)^2=28`

So `x+2=sqrt28=2sqrt7->x=-2+2sqrt7`
Or `x+2=-sqrt28=-2sqrt7->x=-2-2sqrt7`

(sometimes written as `x_(1,2)=-2+-2sqrt7`)