Solve. $LaTeX: \displaystyle \sqrt{x + 32}=\sqrt{x + 8} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 32=x - 4 \sqrt{x + 8} + 12$ . Isolating the radical gives $LaTeX: \displaystyle -5=\sqrt{x + 8}$ Squaring again gives $LaTeX: \displaystyle 25=x + 8$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=17$ . Checking the solution, $LaTeX: \displaystyle x = 17$ , in the original equation gives $LaTeX: \displaystyle 7 = 3$ which is false so it is an extraneous solution and there is no solution.