Solve. $LaTeX: \displaystyle \sqrt{x + 14}=\sqrt{x + 4} + 3$

Squaring both sides gives $LaTeX: \displaystyle x + 14=x + 6 \sqrt{x + 4} + 13$ . Isolating the radical gives $LaTeX: \displaystyle \frac{1}{6}=\sqrt{x + 4}$ Squaring again gives $LaTeX: \displaystyle \frac{1}{36}=x + 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{143}{36}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{143}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{19}{6} = \frac{19}{6}$ which is true so the solution checks.