Solve. $LaTeX: \displaystyle \sqrt{x + 12}=\sqrt{x + 2} + 1$

Squaring both sides gives $LaTeX: \displaystyle x + 12=x + 2 \sqrt{x + 2} + 3$ . Isolating the radical gives $LaTeX: \displaystyle \frac{9}{2}=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle \frac{81}{4}=x + 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{73}{4}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{73}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{11}{2} = \frac{11}{2}$ which is true so the solution checks.