Final answer:
To solve the quadratic equation (x + 1)² + 14 = 15, expand the equation, simplify and factor it, and solve for x to get the solutions.
Step-by-step explanation:
To solve the quadratic equation (x + 1)² + 14 = 15, we can first expand the equation to get x² + 2x + 1 + 14 = 15. Simplifying the equation gives x² + 2x = 0. Next, we move all terms to one side of the equation to get x² + 2x = 0. We can then factor out x from the equation to get x(x + 2) = 0. From here, we have two possibilities: either x = 0 or x + 2 = 0. Solving for x gives us x = 0 or x = -2. Therefore, the solutions to the quadratic equation are x = 0 and x = -2.