Question

What is the solution set for the equation 8 = x^2-2x?

a) {-8,0}
b) {-2,4}
c) {0,2}
d) {-8,-2.4}

Answer 1

The solution set for the equation 8 = x² - 2x is {-2, 4} (option b).

Step-by-step explanation:

The solution set for the equation 8 = x² - 2x can be found by rearranging it into a quadratic equation: x² - 2x - 8 = 0. Now we can use the quadratic formula to solve for the two possible values of x:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values a = 1, b = -2, and c = -8, we get:

x = (-(-2) ± √((-2)² - 4(1)(-8))) / 2(1)

x = (2 ± √(4 + 32)) / 2

x = (2 ± √36) / 2

x = (2 ± 6) / 2

Therefore, the solution set for the equation 8 = x² - 2x is {-2, 4} (option b).