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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{-8±\sqrt{8^{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{-8±8}{2}
Take the square root of 8^{2}.
x=\frac{0}{2}
Now solve the equation x=\frac{-8±8}{2} when ± is plus. Add -8 to 8.
x=0
Divide 0 by 2.
x=-\frac{16}{2}
Now solve the equation x=\frac{-8±8}{2} when ± is minus. Subtract 8 from -8.
x=-8
Divide -16 by 2.
x=0 x=-8
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+4^{2}=4^{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=0 x=-8
Subtract 4 from both sides of the equation.