Final answer:
The solution to the quadratic equation 2x² - 16x + 32 = 0 is x = 4, which is the repeated root because the equation is a perfect square trinomial.
Step-by-step explanation:
The equation 2x² - 16x + 32 = 0 is a quadratic equation of the form ax² + bx + c = 0. To find the solutions to this equation, you can use the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). In this case, a = 2, b = -16, and c = 32.
However, before resorting to the formula, it's worth trying to factor the equation first or recognizing if it's a perfect square trinomial. Factoring reveals that the equation 2x² - 16x + 32 can be rewritten as 2(x² - 8x + 16)
Which upon further simplification becomes 2(x - 4)², indicating that the left side of the equation is a perfect square. Therefore, the solution to this equation is simply x = 4, with this value repeated because both roots are the same.