Final answer:
The solutions to the equation x^2 + 4x = 32 are x = 4 and x = -8.
Step-by-step explanation:
To solve the equation x^2 + 4x = 32, we can rearrange it into a quadratic equation: x^2 + 4x - 32 = 0. Now we can use the quadratic formula to solve for x: x = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 1, b = 4, and c = -32. Plugging in these values, we get x = (-4 ± √(4^2 - 4(1)(-32))) / (2(1)). Simplifying further, we have x = (-4 ± √(16 + 128)) / 2, which becomes x = (-4 ± √144) / 2. Finally, we have x = (-4 ± 12) / 2, giving us two possible solutions: x = (-4 + 12) / 2 = 8/2 = 4 and x = (-4 - 12) / 2 = -16/2 = -8.