Final answer:
To solve the equation 8 = x²-2x, rearrange it into a quadratic equation and use the quadratic formula to find the solution set. The solutions are x = 4 and x = -2.
Step-by-step explanation:
To solve the equation 8 = x²-2x, we can rearrange it into a quadratic equation: x² - 2x - 8 = 0. To find the solution set for this equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a is 1, b is -2, and c is -8.
Plugging these values into the quadratic formula, we get: x = (-(-2) ± √((-2)² - 4(1)(-8))) / (2(1)). Simplifying further, we have: x = (2 ± √(4 + 32)) / 2. This simplifies to: x = (2 ± √36) / 2.
Therefore, the solutions for the equation 8 = x²-2x are: x = (2 + √36) / 2 and x = (2 - √36) / 2. Simplifying these, we get: x = 4 and x = -2.