Question

Solve x^2 + 6x = 7 by completing the square. Which is the solution set of the equation? {–7, 1}

Answer 1

Add 9 to both sides to form a perfect square trinomial:

x² + 6x = 7

x² + 6x + 9 = 16

x² + 2•x•3 + 3² = 16

(x + 3)² = 16

(recall that (a + b)² = a² + 2ab + b²)

Now solve for x. Taking square roots on both sides, we get

x + 3 = ± √16

x + 3 = ± 4

x = -3 ± 4

so the two solutions are x = -7 and x = 1.