Solve. $LaTeX: \displaystyle \sqrt{x + 14}=\sqrt{x + 6} - 4$

Squaring both sides gives $LaTeX: \displaystyle x + 14=x - 8 \sqrt{x + 6} + 22$ . Isolating the radical gives $LaTeX: \displaystyle 1=\sqrt{x + 6}$ Squaring again gives $LaTeX: \displaystyle 1=x + 6$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x=-5$ . Checking the solution, $LaTeX: \displaystyle x = -5$ , in the original equation gives $LaTeX: \displaystyle 3 = -3$ which is false so it is an extraneous solution and there is no solution.