Complete the square and solve: x^2 + 4x - 5 = 0.

• A. -1 or 5
• B. 2 or -4
• C. 1 or -5
• D. 0 or -3

Answer: (C)

Solving a quadratic by completing the square shows how to turn x^2 + 4x into a perfect square, then solve by taking square roots. For the equation x^2 + 4x - 5 = 0, move the constant: x^2 + 4x = 5. To complete the square, add 4, since (4/2)^2 = 4, giving x^2 + 4x + 4 = 9. The left side factors as (x + 2)^2, so (x + 2)^2 = 9. Taking square roots gives x + 2 = ±3, hence x = 1 or x = -5. Checking confirms both work in the original equation, so the solutions are 1 and -5.