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

Squaring both sides gives $LaTeX: \displaystyle x + 18=x - 8 \sqrt{x + 4} + 20$ . 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 $LaTeX: \displaystyle x=- \frac{63}{16}$ . Checking the solution, $LaTeX: \displaystyle x = - \frac{63}{16}$ , in the original equation gives $LaTeX: \displaystyle \frac{15}{4} = - \frac{15}{4}$ which is false so it is an extraneous solution and there is no solution.