Solve. $LaTeX: \displaystyle \sqrt{x + 14}=\sqrt{x + 2} + 3$

Squaring both sides gives $LaTeX: \displaystyle x + 14=x + 6 \sqrt{x + 2} + 11$ . Isolating the radical gives $LaTeX: \displaystyle \frac{1}{2}=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle \frac{1}{4}=x + 2$ . 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 $LaTeX: \displaystyle \frac{7}{2} = \frac{7}{2}$ which is true so the solution checks.