Final answer:
The equation (x - 8)^2 = -25 does not have real solutions, but if we include complex numbers, the solutions are x = 8 + 5i or x = 8 - 5i.
Step-by-step explanation:
To solve the equation provided by the student, which seems to be (x - 8)^2 = -25, we need to start by understanding that this equation has no real solutions because the square of a real number is always non-negative, and thus cannot equal to a negative number like -25.
However, if we look for complex solutions, we can proceed as follows:
- Take the square root on both sides of the equation to obtain x - 8 = ±√-25.
- The square root of -25 can be simplified to 5i, where i is the imaginary unit.
- Thus, the two solutions for x are x = 8 + 5i or x = 8 - 5i.
If this is indeed a typo and the equation should have a positive value on the right-hand side, the process would be similar but would yield real solutions instead of complex ones.