Solve 13x^2-9x

$$13 x ^ { 2 } - 9 x$$

Factor

$$x\left(13x-9\right)$$

Solution Steps

Factor out x.

$$x\left(13x-9\right)$$

Steps Using the Quadratic Formula

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.

$$13x^{2}-9x=0$$

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.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2\times 13}$$

Take the square root of \left(-9\right)^{2}.

$$x=\frac{-\left(-9\right)±9}{2\times 13}$$

The opposite of -9 is 9.

$$x=\frac{9±9}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{9±9}{26}$$

Now solve the equation x=\frac{9±9}{26} when ± is plus. Add 9 to 9.

$$x=\frac{18}{26}$$

Reduce the fraction \frac{18}{26} to lowest terms by extracting and canceling out 2.

$$x=\frac{9}{13}$$

Now solve the equation x=\frac{9±9}{26} when ± is minus. Subtract 9 from 9.

$$x=\frac{0}{26}$$

Divide 0 by 26.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{9}{13} for x_{1} and 0 for x_{2}.

$$13x^{2}-9x=13\left(x-\frac{9}{13}\right)x$$

Subtract \frac{9}{13} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$13x^{2}-9x=13\times \frac{13x-9}{13}x$$

Cancel out 13, the greatest common factor in 13 and 13.

$$13x^{2}-9x=\left(13x-9\right)x$$

Evaluate

$$x\left(13x-9\right)$$