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x\left(2x+5-1\right)=0
Factor out x.
x=0 x=-2
To find equation solutions, solve x=0 and 2x+4=0.
2x^{2}+4x=0
Combine 5x and -x to get 4x.
x=\frac{-4±\sqrt{4^{2}}}{2\times 2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 4 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-4±4}{2\times 2}
Take the square root of 4^{2}.
x=\frac{-4±4}{4}
Multiply 2 times 2.
x=\frac{0}{4}
Now solve the equation x=\frac{-4±4}{4} when ± is plus. Add -4 to 4.
x=0
Divide 0 by 4.
x=-\frac{8}{4}
Now solve the equation x=\frac{-4±4}{4} when ± is minus. Subtract 4 from -4.
x=-2
Divide -8 by 4.
x=0 x=-2
The equation is now solved.
2x^{2}+4x=0
Combine 5x and -x to get 4x.
\frac{2x^{2}+4x}{2}=\frac{0}{2}
Divide both sides by 2.
x^{2}+\frac{4}{2}x=\frac{0}{2}
Dividing by 2 undoes the multiplication by 2.
x^{2}+2x=\frac{0}{2}
Divide 4 by 2.
x^{2}+2x=0
Divide 0 by 2.
x^{2}+2x+1^{2}=1^{2}
Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+2x+1=1
Square 1.
\left(x+1\right)^{2}=1
Factor x^{2}+2x+1. 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+1\right)^{2}}=\sqrt{1}
Take the square root of both sides of the equation.
x+1=1 x+1=-1
Simplify.
x=0 x=-2
Subtract 1 from both sides of the equation.