1. **Problem:** Solve the radical equation $\sqrt{2x} = 12$ and determine if the solution is valid. 2. **Formula and rules:** To solve equations involving square roots, isolate the radical and then square both sides to eliminate the square root. After squaring, check for extraneous solutions by substituting back into the original equation because squaring can introduce invalid solutions. 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 by substituting $x=72$ back into the original equation: $$\sqrt{2 \times 72} = \sqrt{144} = 12$$ This matches the right side, so $x=72$ is a valid solution. **Final answer:** $$x = 72$$