1. **State the problem:** Solve the equation $$\sqrt{x} + 6 = 12$$ for $x$. 2. **Formula and rules:** To solve equations involving square roots, isolate the square root term and then square both sides to eliminate the root. Remember to check for extraneous solutions after squaring. 3. **Isolate the square root:** $$\sqrt{x} = 12 - 6$$ $$\sqrt{x} = 6$$ 4. **Square both sides:** $$\left(\sqrt{x}\right)^2 = 6^2$$ $$x = 36$$ 5. **Check the solution:** Substitute $x=36$ back into the original equation: $$\sqrt{36} + 6 = 6 + 6 = 12$$ which is true. 6. **Final answer:** $$x = 36$$