enter your answer and show all the steps that you use to solve this problem the space provided what are the solutions of the quadratic equation 2X squared -16 X +32 equals zero

Answer 1

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

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -16, and c = 32. Plugging in these values into the quadratic formula, we get:

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

Here, we see that the discriminant (b^2 - 4ac) is zero, indicating that the quadratic equation has exactly one real solution.

Simplifying further, we have:

x = 16/4
x = 4

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