Solve Quadratic Equations Using the Square Root Property: example 10.10

$\begin{array}{c}\begin{array}{cccccc}& & & \hfill {\left(x-2\right)}^2+3& =\hfill & 30\hfill \\ \text{Isolate the binomial term.}\hfill & & & \hfill {\left(x-2\right)}^2& =\hfill & 27\hfill \\ \text{Use the Square Root Property.}\hfill & & & \hfill x-2& =\hfill & \pm \sqrt{27}\hfill \\ \text{Simplify the radical.}\hfill & & & \hfill x-2& =\hfill & \pm 3\sqrt{3}\hfill \\ \text{Solve for}x.\hfill & & & \hfill x& =\hfill & 2\pm 3\sqrt{3}\hfill \end{array}\hfill \\ \\ \text{Rewrite to show two solutions.}x=2+3\sqrt{3},x=2-3\sqrt{3}\hfill \\ \text{Check. We leave the check for you.}\hfill & & \end{array}$