Step-by-step explanation:
x^2 + 8x + 0 = 0
Completing the square just means getting yourself a perfect square trinomial on the left side of your equation. It makes factoring easier for you. The steps are like this:
x² + 8x + 0 = 0 ... take the middle coefficient, 8, divide it by 2, and square it. Same process every time. Divide middle by two, square it. This gives you the "perfect square" of your equation. In this case, 8/2 = 4, and 4² = 16. So what you do is add 16 to BOTH sides of the equation.
x² + 8x + 16 = 16 ... factor the left side
(x + 4)(x + 4) = 16 ... notice that your two factors on the left are identical
(x + 4)² = 16 ... now we want to solve for x. Start by taking the square root of both sides
x + 4 = √16 ... √16 can give us two results: -4 and 4. So solve for both.
x + 4 = 4 x + 4 = -4 ... solve for x
x = 0, x = -8
