Solve -16x^2+72x

$$-16 { x }^{ 2 } +72x$$

Factor

$$8x\left(9-2x\right)$$

Solution Steps

Factor out 8.

$$8\left(-2x^{2}+9x\right)$$

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

$$x\left(-2x+9\right)$$

Rewrite the complete factored expression.

$$8x\left(-2x+9\right)$$

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.

$$-16x^{2}+72x=0$$

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.

$$x=\frac{-72±\sqrt{72^{2}}}{2\left(-16\right)}$$

Take the square root of 72^{2}.

$$x=\frac{-72±72}{2\left(-16\right)}$$

Multiply 2 times -16.

$$x=\frac{-72±72}{-32}$$

Now solve the equation x=\frac{-72±72}{-32} when ± is plus. Add -72 to 72.

$$x=\frac{0}{-32}$$

Divide 0 by -32.

$$x=0$$

Now solve the equation x=\frac{-72±72}{-32} when ± is minus. Subtract 72 from -72.

$$x=-\frac{144}{-32}$$

Reduce the fraction \frac{-144}{-32} to lowest terms by extracting and canceling out 16.

$$x=\frac{9}{2}$$

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

$$-16x^{2}+72x=-16x\left(x-\frac{9}{2}\right)$$

Subtract \frac{9}{2} from x by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$-16x^{2}+72x=-16x\times \frac{-2x+9}{-2}$$

Cancel out 2, the greatest common factor in -16 and -2.

$$-16x^{2}+72x=8x\left(-2x+9\right)$$

Evaluate

$$8x\left(9-2x\right)$$