Question

What are the values of x in the equation x² – 6x + 9 = 25?

1) x = -2 or x = 8
2) x = -1 or x = -11
3) x = 1 or x = 11
4) x = 2 or x = -8

Answer 1

The solutions to the quadratic equation x² – 6x + 9 = 25 are found by simplifying to x² – 6x – 16 = 0 and applying the quadratic formula. The solutions are x = -2 or x = 8.

Step-by-step explanation:

The student is asking for the solutions to the quadratic equation x² – 6x + 9 = 25. This equation can be simplified by subtracting 25 from both sides, resulting in x² – 6x – 16 = 0. Applying the quadratic formula, where a = 1, b = -6, and c = -16, we find that x must satisfy x = [-b ± √(b² - 4ac)] / (2a). Calculating the discriminant, we get √(36 - 4(1)(-16)) = √(100) = 10. Thus, the two solutions are x = (6 ± 10) / 2, which yields x = 8 or x = -2. Therefore, the correct answer is 1) x = -2 or x = 8.