1. The problem states that the square of $(x-2)$ equals 9. This can be written as the equation $$ (x-2)^2 = 9.$$ 2. To solve for $x$, first take the square root of both sides. Remember that when taking the square root, we consider both the positive and negative roots. So, we get: $$ x-2 = \pm 3.$$ 3. Now, split into two cases and solve for $x$: Case 1: $$ x-2 = 3 \implies x = 3 + 2 = 5.$$ Case 2: $$ x-2 = -3 \implies x = -3 + 2 = -1.$$ 4. So, the solutions to the equation are $$ x = 5 $$ and $$ x = -1.$$