Solve (4x^2-72x)

$$( 4 x ^ { 2 } - 72 x )$$

Factor

$$4x\left(x-18\right)$$

Solution Steps

Factor out 4.

$$4\left(x^{2}-18x\right)$$

Consider x^{2}-18x. Factor out x.

$$x\left(x-18\right)$$

Rewrite the complete factored expression.

$$4x\left(x-18\right)$$

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.

$$4x^{2}-72x=0$$

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.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}}}{2\times 4}$$

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

$$x=\frac{-\left(-72\right)±72}{2\times 4}$$

The opposite of -72 is 72.

$$x=\frac{72±72}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{72±72}{8}$$

Now solve the equation x=\frac{72±72}{8} when ± is plus. Add 72 to 72.

$$x=\frac{144}{8}$$

Divide 144 by 8.

$$x=18$$

Now solve the equation x=\frac{72±72}{8} when ± is minus. Subtract 72 from 72.

$$x=\frac{0}{8}$$

Divide 0 by 8.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 18 for x_{1} and 0 for x_{2}.

$$4x^{2}-72x=4\left(x-18\right)x$$

Evaluate

$$4x\left(x-18\right)$$