Are these steps for finding the solutions of $\sqrt{x+3=3−x}$ correct?
- $\sqrt{x+3=3−x}$ is given;
- $x+3=x2−6x+9$, obtained by squaring both sides of(1);
- $0=x2−7x+6$, obtained by subtracting $x+3$ from both sides of(2);
- $0=(x−1)(x−6)$, obtained by factoring the right-hand side of(3);
- $x=1$ or $x=6$,which follows from(4) because $ab=0$ implies that $a=0$ or $b=0$.