Solve for x:
[tex]\begin{gathered} \sqrt[]{x}+2=x \\ \sqrt[]{x}=x-2^{} \\ (\sqrt[]{x})^2=(x-2)^2 \\ x=x^2-4x+4 \\ -x^2+5x-4=0 \\ By\text{ factor left side of equation:} \\ (-x+1)(x-4)=0 \\ \text{Set factor equal to 0} \\ -x+1=0 \\ x=1\text{ } \\ x-4=0 \\ x=4 \end{gathered}[/tex]Now you plug those two values of x in the original equation, since x=1 doesn't work in the original equation, the real solution is x=4 because it works.
