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

Squaring both sides gives $LaTeX: \displaystyle x + 26=x + 4 \sqrt{x - 6} - 2$ . Isolating the radical gives $LaTeX: \displaystyle 7=\sqrt{x - 6}$ Squaring again gives $LaTeX: \displaystyle 49=x - 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=55$ . Checking the solution, $LaTeX: \displaystyle x = 55$ , in the original equation gives $LaTeX: \displaystyle 9 = 9$ which is true so the solution checks.