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x^{2}-6x=0
Subtract 6x from both sides.
x\left(x-6\right)=0
Factor out x.
x=0 x=6
To find equation solutions, solve x=0 and x-6=0.
x^{2}-6x=0
Subtract 6x from both sides.
x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-6\right)±6}{2}
Take the square root of \left(-6\right)^{2}.
x=\frac{6±6}{2}
The opposite of -6 is 6.
x=\frac{12}{2}
Now solve the equation x=\frac{6±6}{2} when ± is plus. Add 6 to 6.
x=6
Divide 12 by 2.
x=\frac{0}{2}
Now solve the equation x=\frac{6±6}{2} when ± is minus. Subtract 6 from 6.
x=0
Divide 0 by 2.
x=6 x=0
The equation is now solved.
x^{2}-6x=0
Subtract 6x from both sides.
x^{2}-6x+\left(-3\right)^{2}=\left(-3\right)^{2}
Divide -6, the coefficient of the x term, by 2 to get -3. Then add the square of -3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-6x+9=9
Square -3.
\left(x-3\right)^{2}=9
Factor x^{2}-6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-3\right)^{2}}=\sqrt{9}
Take the square root of both sides of the equation.
x-3=3 x-3=-3
Simplify.
x=6 x=0
Add 3 to both sides of the equation.