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x\left(x-8\right)=0
Factor out x.
x=0 x=8
To find equation solutions, solve x=0 and x-8=0.
x^{2}-8x=0
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -8 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-8\right)±8}{2}
Take the square root of \left(-8\right)^{2}.
x=\frac{8±8}{2}
The opposite of -8 is 8.
x=\frac{16}{2}
Now solve the equation x=\frac{8±8}{2} when ± is plus. Add 8 to 8.
x=8
Divide 16 by 2.
x=\frac{0}{2}
Now solve the equation x=\frac{8±8}{2} when ± is minus. Subtract 8 from 8.
x=0
Divide 0 by 2.
x=8 x=0
The equation is now solved.
x^{2}-8x=0
Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.
x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}
Divide -8, the coefficient of the x term, by 2 to get -4. Then add the square of -4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-8x+16=16
Square -4.
\left(x-4\right)^{2}=16
Factor x^{2}-8x+16. 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-4\right)^{2}}=\sqrt{16}
Take the square root of both sides of the equation.
x-4=4 x-4=-4
Simplify.
x=8 x=0
Add 4 to both sides of the equation.