Questions: Solve the following quadratic equation by factoring. x^2+12x=-32 The solution set is . (Simplify your answer. Use a comma to separate answers as needed.)

Solution Steps

We start with the given quadratic equation: \[ x^{2} + 12x = -32 \] To rewrite it in standard form, we add \(32\) to both sides: \[ x^{2} + 12x + 32 = 0 \]

Next, we factor the quadratic expression: \[ x^{2} + 12x + 32 = (x + 4)(x + 8) = 0 \]

We set each factor equal to zero:

1. \(x + 4 = 0\) leads to \(x = -4\)
2. \(x + 8 = 0\) leads to \(x = -8\)

Final Answer