Solve. $LaTeX: \displaystyle \sqrt{x + 22}=\sqrt{x + 8} + 2$

Squaring both sides gives $LaTeX: \displaystyle x + 22=x + 4 \sqrt{x + 8} + 12$ . Isolating the radical gives $LaTeX: \displaystyle \frac{5}{2}=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle \frac{25}{4}=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{7}{4}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{7}{4}$ , in the original equation gives $LaTeX: \displaystyle \frac{9}{2} = \frac{9}{2}$ which is true so the solution checks.