1. **State the problem:** Solve the equation $ (x+2)^2 = 64 $. 2. **Recall the formula:** The equation is a quadratic in the form $ (a)^2 = b $, which implies $ a = \pm \sqrt{b} $. 3. **Apply the square root property:** Taking the square root of both sides gives $$ x+2 = \pm \sqrt{64} $$ 4. **Simplify the square root:** Since $ \sqrt{64} = 8 $, we have $$ x+2 = \pm 8 $$ 5. **Solve for $x$ in both cases:** - Case 1: $ x+2 = 8 \Rightarrow x = 8 - 2 = 6 $ - Case 2: $ x+2 = -8 \Rightarrow x = -8 - 2 = -10 $ 6. **Final answer:** The solutions are $$ x = 6 \text{ or } x = -10 $$