Answer
{$0,6$}
Work Step by Step
Step 1: $x^{2}-6x=0$ can also be written as $x^{2}-6x+0=0$. Comparing $x^{2}-6x+0=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain:
$a=1$, $b=-6$ and $c=0$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a,b, and c in the formula, we obtain:
$x=\frac{-(-6) \pm \sqrt {(-6)^{2}-4(1)(0)}}{2(1)}$
Step 4: $x=\frac{6 \pm \sqrt {36-0}}{2}$
Step 5: $x=\frac{6 \pm \sqrt {36}}{2}$
Step 6: $x=\frac{6 \pm 6}{2}$
Step 7: $x=\frac{6+6}{2}$ or $x=\frac{6-6}{2}$
Step 8: $x=\frac{12}{2}$ or $x=\frac{0}{2}$
Step 9: $x=6$ or $x=0$
Step 10: Therefore, the solution set is {$0,6$}.
