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

Squaring both sides gives $LaTeX: \displaystyle x + 14=x + 8 \sqrt{x - 4} + 12$ . Isolating the radical gives $LaTeX: \displaystyle \frac{1}{4}=\sqrt{x - 4}$ Squaring again gives $LaTeX: \displaystyle \frac{1}{16}=x - 4$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{65}{16}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{65}{16}$ , in the original equation gives $LaTeX: \displaystyle \frac{17}{4} = \frac{17}{4}$ which is true so the solution checks.