Solve. $LaTeX: \displaystyle \sqrt{x + 18}=\sqrt{x + 8} + 4$

Squaring both sides gives $LaTeX: \displaystyle x + 18=x + 8 \sqrt{x + 8} + 24$ . Isolating the radical gives $LaTeX: \displaystyle - \frac{3}{4}=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle \frac{9}{16}=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=- \frac{119}{16}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{119}{16}$ , in the original equation gives $LaTeX: \displaystyle \frac{13}{4} = \frac{19}{4}$ which is false so it is an extraneous solution and there is no solution.