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

Squaring both sides gives $LaTeX: \displaystyle x + 26=x - 4 \sqrt{x + 2} + 6$ . Isolating the radical gives $LaTeX: \displaystyle -5=\sqrt{x + 2}$ Squaring again gives $LaTeX: \displaystyle 25=x + 2$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=23$ . Checking the solution, $LaTeX: \displaystyle x = 23$ , in the original equation gives $LaTeX: \displaystyle 7 = 3$ which is false so it is an extraneous solution and there is no solution.