Factor
4\left(x-\frac{-\sqrt{41}-3}{8}\right)\left(x-\frac{\sqrt{41}-3}{8}\right)
Evaluate
4x^{2}+3x-2
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factor(4x^{2}+3x-2)
Calculate 2 to the power of 2 and get 4.
4x^{2}+3x-2=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-3±\sqrt{3^{2}-4\times 4\left(-2\right)}}{2\times 4}
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{-3±\sqrt{9-4\times 4\left(-2\right)}}{2\times 4}
Square 3.
x=\frac{-3±\sqrt{9-16\left(-2\right)}}{2\times 4}
Multiply -4 times 4.
x=\frac{-3±\sqrt{9+32}}{2\times 4}
Multiply -16 times -2.
x=\frac{-3±\sqrt{41}}{2\times 4}
Add 9 to 32.
x=\frac{-3±\sqrt{41}}{8}
Multiply 2 times 4.
x=\frac{\sqrt{41}-3}{8}
Now solve the equation x=\frac{-3±\sqrt{41}}{8} when ± is plus. Add -3 to \sqrt{41}.
x=\frac{-\sqrt{41}-3}{8}
Now solve the equation x=\frac{-3±\sqrt{41}}{8} when ± is minus. Subtract \sqrt{41} from -3.
4x^{2}+3x-2=4\left(x-\frac{\sqrt{41}-3}{8}\right)\left(x-\frac{-\sqrt{41}-3}{8}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{41}}{8} for x_{1} and \frac{-3-\sqrt{41}}{8} for x_{2}.
4x^{2}+3x-2
Calculate 2 to the power of 2 and get 4.
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}