Solve. $LaTeX: \displaystyle \sqrt{x + 16}=\sqrt{x + 6} - 4$

Squaring both sides gives $LaTeX: \displaystyle x + 16=x - 8 \sqrt{x + 6} + 22$ . Isolating the radical gives $LaTeX: \displaystyle \frac{3}{4}=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle \frac{9}{16}=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{87}{16}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{87}{16}$ , in the original equation gives $LaTeX: \displaystyle \frac{13}{4} = - \frac{13}{4}$ which is false so it is an extraneous solution and there is no solution.