Solve 45x^2-20x

$$45 x ^ { 2 } - 20 x$$

Factor

$$5x\left(9x-4\right)$$

Solution Steps

Factor out 5.

$$5\left(9x^{2}-4x\right)$$

Consider 9x^{2}-4x. Factor out x.

$$x\left(9x-4\right)$$

Rewrite the complete factored expression.

$$5x\left(9x-4\right)$$

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.

$$45x^{2}-20x=0$$

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.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}}}{2\times 45}$$

Take the square root of \left(-20\right)^{2}.

$$x=\frac{-\left(-20\right)±20}{2\times 45}$$

The opposite of -20 is 20.

$$x=\frac{20±20}{2\times 45}$$

Multiply 2 times 45.

$$x=\frac{20±20}{90}$$

Now solve the equation x=\frac{20±20}{90} when ± is plus. Add 20 to 20.

$$x=\frac{40}{90}$$

Reduce the fraction \frac{40}{90} to lowest terms by extracting and canceling out 10.

$$x=\frac{4}{9}$$

Now solve the equation x=\frac{20±20}{90} when ± is minus. Subtract 20 from 20.

$$x=\frac{0}{90}$$

Divide 0 by 90.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{4}{9} for x_{1} and 0 for x_{2}.

$$45x^{2}-20x=45\left(x-\frac{4}{9}\right)x$$

Subtract \frac{4}{9} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$45x^{2}-20x=45\times \frac{9x-4}{9}x$$

Cancel out 9, the greatest common factor in 45 and 9.

$$45x^{2}-20x=5\left(9x-4\right)x$$

Evaluate

$$5x\left(9x-4\right)$$