Solve by completing the square. x² + 4x = 12 A) x = 2, x = -6 B) x = 2, x = 6 C) x = -2, x = -6 D) x = -2, x = 6

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 4x = 12$ by completing the square, first move the constant term to the other side: $x^2 + 4x - 12 = 0$. Then, add $(\frac{4}{2})^2 = 4$ to both sides to complete the square: $x^2 + 4x + 4 = 12 + 4$, which simplifies to $x^2 + 4x + 4 = 16$. This can be written as $(x + 2)^2 = 16$. Taking the square root of both sides gives $x + 2 = \pm4$, leading to two solutions: $x = 2$ and $x = -6$.

Solve by Completing the Square