Enter your answer and show all the steps that you use to solve this problem in the space provided.

Question

What are the solutions of the quadratic equation?
2x^2 - 16x + 32 = 0

Answer 1

To find the solutions of the quadratic equation 2x^2 - 16x + 32 = 0, we can use the quadratic formula.

The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

For our equation 2x^2 - 16x + 32 = 0, we have a = 2, b = -16, and c = 32.

Plugging these values into the quadratic formula, we get:

x = (-(-16) ± sqrt((-16)^2 - 4(2)(32))) / (2(2))
= (16 ± sqrt(256 - 256)) / 4
= (16 ± sqrt(0)) / 4

Since the discriminant, which is the term inside the square root, is equal to 0, we have a unique solution. This means that the quadratic equation has one real root.

Simplifying further, we have:

x = (16 ± 0) / 4
= 16/4
= 4

Therefore, the solution to the quadratic equation 2x^2 - 16x + 32 = 0 is x = 4.