Solve for x (complex solution)
x=\sqrt{13}-1\approx 2.605551275
x=-\left(\sqrt{13}+1\right)\approx -4.605551275
Solve for x
x=\sqrt{13}-1\approx 2.605551275
x=-\sqrt{13}-1\approx -4.605551275
Graph
Share
Copied to clipboard
x^{2}+2x-12=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{-2±\sqrt{2^{2}-4\left(-12\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-2±\sqrt{4-4\left(-12\right)}}{2}
Square 2.
x=\frac{-2±\sqrt{4+48}}{2}
Multiply -4 times -12.
x=\frac{-2±\sqrt{52}}{2}
Add 4 to 48.
x=\frac{-2±2\sqrt{13}}{2}
Take the square root of 52.
x=\frac{2\sqrt{13}-2}{2}
Now solve the equation x=\frac{-2±2\sqrt{13}}{2} when ± is plus. Add -2 to 2\sqrt{13}.
x=\sqrt{13}-1
Divide -2+2\sqrt{13} by 2.
x=\frac{-2\sqrt{13}-2}{2}
Now solve the equation x=\frac{-2±2\sqrt{13}}{2} when ± is minus. Subtract 2\sqrt{13} from -2.
x=-\sqrt{13}-1
Divide -2-2\sqrt{13} by 2.
x=\sqrt{13}-1 x=-\sqrt{13}-1
The equation is now solved.
x^{2}+2x-12=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}+2x-12-\left(-12\right)=-\left(-12\right)
Add 12 to both sides of the equation.
x^{2}+2x=-\left(-12\right)
Subtracting -12 from itself leaves 0.
x^{2}+2x=12
Subtract -12 from 0.
x^{2}+2x+1^{2}=12+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=12+1
Square 1.
x^{2}+2x+1=13
Add 12 to 1.
\left(x+1\right)^{2}=13
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{13}
Take the square root of both sides of the equation.
x+1=\sqrt{13} x+1=-\sqrt{13}
Simplify.
x=\sqrt{13}-1 x=-\sqrt{13}-1
Subtract 1 from both sides of the equation.
x^{2}+2x-12=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{-2±\sqrt{2^{2}-4\left(-12\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-2±\sqrt{4-4\left(-12\right)}}{2}
Square 2.
x=\frac{-2±\sqrt{4+48}}{2}
Multiply -4 times -12.
x=\frac{-2±\sqrt{52}}{2}
Add 4 to 48.
x=\frac{-2±2\sqrt{13}}{2}
Take the square root of 52.
x=\frac{2\sqrt{13}-2}{2}
Now solve the equation x=\frac{-2±2\sqrt{13}}{2} when ± is plus. Add -2 to 2\sqrt{13}.
x=\sqrt{13}-1
Divide -2+2\sqrt{13} by 2.
x=\frac{-2\sqrt{13}-2}{2}
Now solve the equation x=\frac{-2±2\sqrt{13}}{2} when ± is minus. Subtract 2\sqrt{13} from -2.
x=-\sqrt{13}-1
Divide -2-2\sqrt{13} by 2.
x=\sqrt{13}-1 x=-\sqrt{13}-1
The equation is now solved.
x^{2}+2x-12=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}+2x-12-\left(-12\right)=-\left(-12\right)
Add 12 to both sides of the equation.
x^{2}+2x=-\left(-12\right)
Subtracting -12 from itself leaves 0.
x^{2}+2x=12
Subtract -12 from 0.
x^{2}+2x+1^{2}=12+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=12+1
Square 1.
x^{2}+2x+1=13
Add 12 to 1.
\left(x+1\right)^{2}=13
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{13}
Take the square root of both sides of the equation.
x+1=\sqrt{13} x+1=-\sqrt{13}
Simplify.
x=\sqrt{13}-1 x=-\sqrt{13}-1
Subtract 1 from both sides of the equation.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}