## Elementary Algebra

$x=2$
Using the properties of equality, the given equation, $\sqrt{8x}-2=x ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{8x}=x+2 .\end{array} Squaring both sides of the equation and then using the properties of equality, we obtain: \begin{array}{l}\require{cancel}\left( \sqrt{8x} \right)^2=\left( x+2 \right)^2 \\\\ 8x=(x)^2+2(x)(2)+(2)^2 \\\\ 8x=x^2+4x+4 \\\\ 0=x^2+(4x-8x)+4 \\\\ x^2-4x+4=0 \\\\ (x-2)^2=0 \\\\ x=2 .\end{array} Upon checking, $x=2$ satisfies the original equation.