Solving the Equation (x  8)² = 81
This equation involves a squared term, which means we'll need to use the square root property to solve for x. Here's a stepbystep guide:
1. Take the Square Root of Both Sides
The square root property states that if two expressions are equal, then their square roots are also equal. So, we take the square root of both sides of the equation:
√((x  8)²) = ±√81
This gives us:
x  8 = ±9
2. Solve for x
Now we have two separate equations to solve:
 Equation 1: x  8 = 9
 Equation 2: x  8 = 9
Solving for x in each equation:

Equation 1:
 x = 9 + 8
 x = 17

Equation 2:
 x = 9 + 8
 x = 1
Conclusion
Therefore, the solutions to the equation (x  8)² = 81 are x = 17 and x = 1.