Solve 252x^2-72x

$$252 x ^ { 2 } - 72 x$$

Factor

$$36x\left(7x-2\right)$$

Solution Steps

Factor out 36.

$$36\left(7x^{2}-2x\right)$$

Consider 7x^{2}-2x. Factor out x.

$$x\left(7x-2\right)$$

Rewrite the complete factored expression.

$$36x\left(7x-2\right)$$

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.

$$252x^{2}-72x=0$$

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.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}}}{2\times 252}$$

Take the square root of \left(-72\right)^{2}.

$$x=\frac{-\left(-72\right)±72}{2\times 252}$$

The opposite of -72 is 72.

$$x=\frac{72±72}{2\times 252}$$

Multiply 2 times 252.

$$x=\frac{72±72}{504}$$

Now solve the equation x=\frac{72±72}{504} when ± is plus. Add 72 to 72.

$$x=\frac{144}{504}$$

Reduce the fraction \frac{144}{504} to lowest terms by extracting and canceling out 72.

$$x=\frac{2}{7}$$

Now solve the equation x=\frac{72±72}{504} when ± is minus. Subtract 72 from 72.

$$x=\frac{0}{504}$$

Divide 0 by 504.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{2}{7} for x_{1} and 0 for x_{2}.

$$252x^{2}-72x=252\left(x-\frac{2}{7}\right)x$$

Subtract \frac{2}{7} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$252x^{2}-72x=252\times \frac{7x-2}{7}x$$

Cancel out 7, the greatest common factor in 252 and 7.

$$252x^{2}-72x=36\left(7x-2\right)x$$

Evaluate

$$36x\left(7x-2\right)$$