Question

How do you solve `x^2 + 4x - 12= 0` using completing the square?

Answer 1

`0 = x^2+4x-12 = (x+2)^2-4-12 = (x+2)^2-16`
`= (x+2)^2 - 4^2`

Hence `x = -2 +- 4`

That is `x = -6` or `x = 2`

Explanation:

`(x+2)^2 = x^2+4x+4`

So:

`0 = x^2+4x-12 = x^2+4x+4-4-12`

`=(x+2)^2-4-12 = (x+2)^2-16 = (x+2)^2-4^2`

Add `4^2` to both ends to get:

`(x+2)^2 = 4^2`

Hence:

`x+2 = +-4`

Subtract `2` from both sides to get:

`x = -2+-4`