To solve the equation |x-2| = (-3)^2, we first simplify the right side of the equation.

(-3)^2 = 9

Now, we can rewrite the equation as |x-2| = 9.

To solve for x, we consider two cases:

Case 1: (x-2) is positive or zero.
In this case, the equation |x-2| = 9 becomes x-2 = 9.
Solving for x, we add 2 to both sides of the equation:
x - 2 + 2 = 9 + 2
x = 11

Case 2: (x-2) is negative.
In this case, the equation |x-2| = 9 becomes -(x-2) = 9.
Solving for x, we distribute the negative sign:
-x + 2 = 9
Subtracting 2 from both sides of the equation:
-x + 2 - 2 = 9 - 2
-x = 7
Multiplying both sides of the equation by -1 to isolate x:
(-1)(-x) = (-1)(7)
x = -7

Therefore, the solutions to the equation |x-2| = 9 are x = 11 and x = -7.