1. **State the problem:** Solve the equation $$\sqrt{4x+36}+2=10$$ for $x$. 2. **Isolate the square root term:** Subtract 2 from both sides: $$\sqrt{4x+36}+2-2=10-2$$ $$\sqrt{4x+36}=8$$ 3. **Square both sides to eliminate the square root:** $$\left(\sqrt{4x+36}\right)^2=8^2$$ $$4x+36=64$$ 4. **Solve for $x$:** Subtract 36 from both sides: $$4x+\cancel{36}-\cancel{36}=64-36$$ $$4x=28$$ Divide both sides by 4: $$\frac{4x}{\cancel{4}}=\frac{28}{\cancel{4}}$$ $$x=7$$ 5. **Check the solution:** Substitute $x=7$ back into the original equation: $$\sqrt{4(7)+36}+2=\sqrt{28+36}+2=\sqrt{64}+2=8+2=10$$ The left side equals the right side, so $x=7$ is the correct solution. **Final answer:** $$x=7$$