Nonlinear Equations in One Variable and Systems of Equations

Square: $x + 3 = x^2 - 6x + 9 \Rightarrow x^2 - 7x + 6 = 0 \Rightarrow (x-6)(x-1)$. Check $x=1$: $\sqrt{4}=2$, but $1-3=-2$, extraneous. $x=6$: $\sqrt{9}=3=6-3$, valid. One real solution.