1. **State the problem:** Solve the equation $5(x - 4)^2 = 30$ for $x$. 2. **Isolate the squared term:** Divide both sides by 5 to simplify. $$5(x - 4)^2 = 30$$ $$\cancel{5}(x - 4)^2 = \cancel{5}6$$ $$ (x - 4)^2 = 6 $$ 3. **Take the square root of both sides:** Remember to consider both positive and negative roots. $$x - 4 = \pm \sqrt{6}$$ 4. **Solve for $x$:** Add 4 to both sides. $$x = 4 \pm \sqrt{6}$$ 5. **Final answer:** The solutions are $$x = 4 + \sqrt{6} \quad \text{or} \quad x = 4 - \sqrt{6}$$ This means $x$ can be either $4 + \sqrt{6}$ or $4 - \sqrt{6}$, which are the two values that satisfy the original equation.