Question

Solve x^2 + 12x = -20 by completing the square.

Add (b/2)^2 to both sides of the equation. The value of (b/2)^2 in this equation is___.

Answer 1

x = - 10, x = - 2

Explanation:

Given

x² + 12x = - 20

To complete the square

add (half the coefficient of the x- term )² to both sides

x² + 2(6)x + 6² = - 20 + 6² ← completing the square

(x + 6)² = - 20 + 36 = 16

Take the square root of both sides

x + 6 = ±
`√(16)` = ± 4

Subtract 6 from both sides

x = - 6 ± 4, hence

x = - 6 - 4 = - 10 or x = - 6 + 4 = - 2