Question

How do you complete the square for `: x^2 + 6x`?

Answer 1

`(x+3)^2 = x^2+6x+9`

So `x^2 +6x = (x+3)^2 - 9`

If you were actually trying to solve `x^2+6x=0`, then completing the square would be a round about way of doing it, but would look something like this:

`0 = x^2+6x = x^2+6x+9-9 = (x+3)^2-9`

Adding 9 to both sides you get `(x+3)^2 = 9`

So `x+3 = +-sqrt(9) = +-3`

Then subtracting 3 from both sides, you get

`x = -3+-3`

In other words `x = 0` or `x = -6`.