Solve 9x^2+48x-64

$$9 { x }^{ 2 } +48x-64$$

Factor

$$9\left(x-\frac{-8\sqrt{2}-8}{3}\right)\left(x-\frac{8\sqrt{2}-8}{3}\right)$$

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.

$$9x^{2}+48x-64=0$$

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.

$$x=\frac{-48±\sqrt{48^{2}-4\times 9\left(-64\right)}}{2\times 9}$$

Square 48.

$$x=\frac{-48±\sqrt{2304-4\times 9\left(-64\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{-48±\sqrt{2304-36\left(-64\right)}}{2\times 9}$$

Multiply -36 times -64.

$$x=\frac{-48±\sqrt{2304+2304}}{2\times 9}$$

Add 2304 to 2304.

$$x=\frac{-48±\sqrt{4608}}{2\times 9}$$

Take the square root of 4608.

$$x=\frac{-48±48\sqrt{2}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{-48±48\sqrt{2}}{18}$$

Now solve the equation x=\frac{-48±48\sqrt{2}}{18} when ± is plus. Add -48 to 48\sqrt{2}.

$$x=\frac{48\sqrt{2}-48}{18}$$

Divide -48+48\sqrt{2} by 18.

$$x=\frac{8\sqrt{2}-8}{3}$$

Now solve the equation x=\frac{-48±48\sqrt{2}}{18} when ± is minus. Subtract 48\sqrt{2} from -48.

$$x=\frac{-48\sqrt{2}-48}{18}$$

Divide -48-48\sqrt{2} by 18.

$$x=\frac{-8\sqrt{2}-8}{3}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-8+8\sqrt{2}}{3} for x_{1} and \frac{-8-8\sqrt{2}}{3} for x_{2}.

$$9x^{2}+48x-64=9\left(x-\frac{8\sqrt{2}-8}{3}\right)\left(x-\frac{-8\sqrt{2}-8}{3}\right)$$

Evaluate

$$9x^{2}+48x-64$$