Solve for x
x=-12
x=0
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x\left(x+12\right)=0
Factor out x.
x=0 x=-12
To find equation solutions, solve x=0 and x+12=0.
x^{2}+12x=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{-12±\sqrt{12^{2}}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 12 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-12±12}{2}
Take the square root of 12^{2}.
x=\frac{0}{2}
Now solve the equation x=\frac{-12±12}{2} when ± is plus. Add -12 to 12.
x=0
Divide 0 by 2.
x=-\frac{24}{2}
Now solve the equation x=\frac{-12±12}{2} when ± is minus. Subtract 12 from -12.
x=-12
Divide -24 by 2.
x=0 x=-12
The equation is now solved.
x^{2}+12x=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}+12x+6^{2}=6^{2}
Divide 12, the coefficient of the x term, by 2 to get 6. Then add the square of 6 to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}+12x+36=36
Square 6.
\left(x+6\right)^{2}=36
Factor x^{2}+12x+36. 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+6\right)^{2}}=\sqrt{36}
Take the square root of both sides of the equation.
x+6=6 x+6=-6
Simplify.
x=0 x=-12
Subtract 6 from both sides of the equation.
Examples
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Linear equation
y = 3x + 4
Arithmetic
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}