Final answer:
To solve the equation x² - 6x + 9 = 25, we rearrange it to x² - 6x - 16 = 0 and apply the quadratic formula, resulting in two solutions for x: x = 8 and x = -2.
Step-by-step explanation:
To find the values of x in the equation x² - 6x + 9 = 25, we first need to rearrange it into standard quadratic form ax² + bx + c = 0. Subtracting 25 from both sides of the equation gives us x² - 6x - 16 = 0. We can then solve this equation using the quadratic formula, x = [-b ± √(b² - 4ac)]/(2a), where a = 1, b = -6, and c = -16.
Plugging these values into the formula, we get:
- x = [6 ± √(36 + 64)]/2
- x = [6 ± √100]/2
- x = [6 ± 10]/2
This yields two solutions:
- x = (6 + 10)/2 = 16/2 = 8
- x = (6 - 10)/2 = -4/2 = -2
Therefore, the values of x are x = 8 and x = -2.