## Intermediate Algebra (6th Edition)

$x=5$
Using the properties of equality, the given equation, $\sqrt{2x-1}+2=x ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{2x-1}=x-2 .\end{array} Raising both sides to the second power, then the solution/s to the equation above is/are \begin{array}{l}\require{cancel} 2x-1=(x-2)^2 \\\\ 2x-1=(x)^2+2(x)(-2)+(-2)^2 \\\\ 2x-1=x^2-4x+4 \\\\ -x^2+(2x+4x)+(-1-4)=0 \\\\ -x^2+6x-5=0 \\\\ x^2-6x+5=0 \\\\ (x-5)(x-1)=0 \\\\ x=\left\{ 1,5 \right\} .\end{array} Upon checking, only $x=5$ satisfies the original equation.