1. **State the problem:** Solve the inequality $ (x-2)^2 \leq 0 $. 2. **Recall the property of squares:** For any real number $a$, $a^2 \geq 0$ and $a^2 = 0$ if and only if $a=0$. 3. **Apply this to the inequality:** Since $ (x-2)^2 \leq 0 $, the only way this can be true is if $ (x-2)^2 = 0 $. 4. **Solve the equation:** $$ (x-2)^2 = 0 $$ Taking the square root of both sides, $$ \sqrt{(x-2)^2} = \sqrt{0} $$ $$ |x-2| = 0 $$ This implies $$ x-2 = 0 $$ 5. **Find the solution:** $$ x = 2 $$ 6. **Conclusion:** The inequality $ (x-2)^2 \leq 0 $ holds only at $x=2$. For all other values of $x$, $ (x-2)^2 > 0 $. **Final answer:** $$ x = 2 $$