Factor
x\left(4x-13\right)
Evaluate
x\left(4x-13\right)
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x\left(4x-13\right)
Factor out x.
4x^{2}-13x=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{-\left(-13\right)±\sqrt{\left(-13\right)^{2}}}{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{-\left(-13\right)±13}{2\times 4}
Take the square root of \left(-13\right)^{2}.
x=\frac{13±13}{2\times 4}
The opposite of -13 is 13.
x=\frac{13±13}{8}
Multiply 2 times 4.
x=\frac{26}{8}
Now solve the equation x=\frac{13±13}{8} when ± is plus. Add 13 to 13.
x=\frac{13}{4}
Reduce the fraction \frac{26}{8} to lowest terms by extracting and canceling out 2.
x=\frac{0}{8}
Now solve the equation x=\frac{13±13}{8} when ± is minus. Subtract 13 from 13.
x=0
Divide 0 by 8.
4x^{2}-13x=4\left(x-\frac{13}{4}\right)x
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{13}{4} for x_{1} and 0 for x_{2}.
4x^{2}-13x=4\times \frac{4x-13}{4}x
Subtract \frac{13}{4} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.
4x^{2}-13x=\left(4x-13\right)x
Cancel out 4, the greatest common factor in 4 and 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}