1. **State the problem:** Solve the equation $$(x - 3)^2 = 24$$ for $x$. 2. **Recall the formula:** To solve an equation of the form $$(x - a)^2 = b$$, take the square root of both sides: $$x - a = \pm \sqrt{b}$$ 3. **Apply the formula:** Here, $a = 3$ and $b = 24$, so $$x - 3 = \pm \sqrt{24}$$ 4. **Simplify the square root:** $$\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}$$ 5. **Write the solutions:** $$x - 3 = \pm 2\sqrt{6}$$ 6. **Isolate $x$:** $$x = 3 \pm 2\sqrt{6}$$ **Final answer:** $$x = 3 + 2\sqrt{6} \quad \text{or} \quad x = 3 - 2\sqrt{6}$$