1. **Problem statement:** Solve the radical equation $\sqrt{2x} = 12$ and determine if the solution is acceptable. 2. **Formula and rules:** To solve equations involving square roots, isolate the square root expression and then square both sides to eliminate the root. Remember to check for extraneous solutions because squaring can introduce invalid answers. 3. **Step-by-step solution:** 1. Start with the equation: $$\sqrt{2x} = 12$$ 2. Square both sides to remove the square root: $$\left(\sqrt{2x}\right)^2 = 12^2$$ $$2x = 144$$ 3. Solve for $x$: $$x = \frac{144}{2} = 72$$ 4. **Check the solution:** Substitute $x=72$ back into the original equation: $$\sqrt{2 \times 72} = \sqrt{144} = 12$$ This matches the right side, so $x=72$ is an acceptable solution. **Final answer:** $$x = 72$$