Solve. $LaTeX: \displaystyle \sqrt{x + 32}=\sqrt{x + 2} - 4$

Squaring both sides gives $LaTeX: \displaystyle x + 32=x - 8 \sqrt{x + 2} + 18$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{7}{4}=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle \frac{49}{16}=x + 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=\frac{17}{16}$ . Checking the solution, $LaTeX: \displaystyle x = \frac{17}{16}$ , in the original equation gives $LaTeX: \displaystyle \frac{23}{4} = - \frac{9}{4}$ which is false so it is an extraneous solution and there is no solution.