Question

2. Noah is solving the equation x² + 8x + 15 = 3. He begins by rewriting the

expression on the left in factored form and writes (x + 3)(x + 5) = 3. He
does not know what to do next.
Noah knows that the solutions are x = -2 and x = -6, but is not sure how
get to these values from his equation.
Solve the original equation by completing the square.

Answer 1

The solution set is {-6, -2}.

Explanation:

x^2 + 8x + 15 = 3

x^2 + 8x = -12

Completing the square:

(x + 4)^2 - 16 = -12

(x + 4)^2 = 4

Taking square roots of both sides:

x + 4 = +/- 2

x = 2 - 4 = -2 or x = -2-4 = -6.