Solve. $LaTeX: \displaystyle \sqrt{x + 26}=\sqrt{x + 6} - 2$

Squaring both sides gives $LaTeX: \displaystyle x + 26=x - 4 \sqrt{x + 6} + 10$ . Isolating the radical gives $LaTeX: \displaystyle -4=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle 16=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=10$ . Checking the solution, $LaTeX: \displaystyle x = 10$ , in the original equation gives $LaTeX: \displaystyle 6 = 2$ which is false so it is an extraneous solution and there is no solution.