Solve. $LaTeX: \displaystyle \sqrt{x + 14}=\sqrt{x + 6} + 3$

Squaring both sides gives $LaTeX: \displaystyle x + 14=x + 6 \sqrt{x + 6} + 15$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{1}{6}=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle \frac{1}{36}=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{215}{36}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{215}{36}$ , in the original equation gives $LaTeX: \displaystyle \frac{17}{6} = \frac{19}{6}$ which is false so it is an extraneous solution and there is no solution.