## Algebra: A Combined Approach (4th Edition)

$x=\left\{ 1-2\sqrt{2},1+2\sqrt{2} \right\}$
$\bf{\text{Solution Outline:}}$ To solve the given equation, $(x-1)^2=8 ,$ take the square root of both sides and simplify the resulting radical. Then use the properties of equality to isolate the variable. $\bf{\text{Solution Details:}}$ Taking the square root of both sides (Square Root Property), the equation above is equivalent to \begin{array}{l}\require{cancel} x-1=\pm\sqrt{8} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} x-1=\pm\sqrt{4\cdot2} \\\\ x-1=\pm\sqrt{(2)^2\cdot2} \\\\ x-1=\pm2\sqrt{2} .\end{array} Using the properties of equality to isolate the variable results to \begin{array}{l}\require{cancel} x=1\pm2\sqrt{2} .\end{array} Hence the solutions are $x=\left\{ 1-2\sqrt{2},1+2\sqrt{2} \right\} .$