Question

Solve x2 + 4x – 12 = 0 by completing the square. Show your work for full credit.

Answer 1

Looking at the formula, you know you're going to start with:

(x )(x )

Since that's the only way you can get x^2. You have a couple of ways you can get 12: 2 x 6 or 3 x 4 or 1 x 12. Only one of these gives you a way to get 4 (4x) though: 2 x 6. So now we have:

(x 2)(x 6)

The last step is to figure out the signs. We want -12 but +4 so we know one will be positive and one negative. To get +4 we need a +6 and -2 so we end up with:

(x - 2)(x + 6)