Final answer:
To solve the quadratic equation w^2 + 5w - 32 = 2w - 4 by completing the square, we rearrange the equation, create a perfect square trinomial, and solve for w.
Step-by-step explanation:
To solve the quadratic equation by completing the square, we need to rearrange the equation to have the form ax^2 + bx + c = 0. In this case, the equation is w^2 + 5w - 32 = 2w - 4. Let's begin by subtracting 2w from both sides to get w^2 + 3w - 32 = -4. Next, we add 36 to both sides to create a perfect square trinomial on the left side: w^2 + 3w + 4 = 0.
Now, we can factor the left side of the equation: (w + 4)(w + 1) = 0. Setting each factor equal to zero, we have two possible solutions: w + 4 = 0 or w + 1 = 0. Solving for w in each equation gives us w = -4 or w = -1. Therefore, the roots of the quadratic equation are -4 and -1.