1. **Stating the problem:** Solve the equation $$\sqrt{x} + 5 = 3\sqrt{x} - 3$$ 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 term:** $$\sqrt{x} + 5 = 3\sqrt{x} - 3$$ Subtract $\sqrt{x}$ from both sides: $$5 = 2\sqrt{x} - 3$$ Add 3 to both sides: $$5 + 3 = 2\sqrt{x}$$ $$8 = 2\sqrt{x}$$ 4. **Divide both sides by 2:** $$\frac{8}{2} = \cancel{2}\sqrt{x} \div \cancel{2}$$ $$4 = \sqrt{x}$$ 5. **Square both sides to solve for $x$:** $$4^2 = (\sqrt{x})^2$$ $$16 = x$$ 6. **Check the solution:** Substitute $x=16$ back into the original equation: $$\sqrt{16} + 5 = 3\sqrt{16} - 3$$ $$4 + 5 = 3 \times 4 - 3$$ $$9 = 12 - 3$$ $$9 = 9$$ True, so $x=16$ is the solution. **Final answer:** $$x = 16$$