Solve 9x^2+72x-336

$$9 { x }^{ 2 } +72x-336$$

Factor

$$9\left(x-\left(-\frac{4\sqrt{30}}{3}-4\right)\right)\left(x-\left(\frac{4\sqrt{30}}{3}-4\right)\right)$$

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.

$$9x^{2}+72x-336=0$$

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.

$$x=\frac{-72±\sqrt{72^{2}-4\times 9\left(-336\right)}}{2\times 9}$$

Square 72.

$$x=\frac{-72±\sqrt{5184-4\times 9\left(-336\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{-72±\sqrt{5184-36\left(-336\right)}}{2\times 9}$$

Multiply -36 times -336.

$$x=\frac{-72±\sqrt{5184+12096}}{2\times 9}$$

Add 5184 to 12096.

$$x=\frac{-72±\sqrt{17280}}{2\times 9}$$

Take the square root of 17280.

$$x=\frac{-72±24\sqrt{30}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{-72±24\sqrt{30}}{18}$$

Now solve the equation x=\frac{-72±24\sqrt{30}}{18} when ± is plus. Add -72 to 24\sqrt{30}.

$$x=\frac{24\sqrt{30}-72}{18}$$

Divide -72+24\sqrt{30} by 18.

$$x=\frac{4\sqrt{30}}{3}-4$$

Now solve the equation x=\frac{-72±24\sqrt{30}}{18} when ± is minus. Subtract 24\sqrt{30} from -72.

$$x=\frac{-24\sqrt{30}-72}{18}$$

Divide -72-24\sqrt{30} by 18.

$$x=-\frac{4\sqrt{30}}{3}-4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -4+\frac{4\sqrt{30}}{3} for x_{1} and -4-\frac{4\sqrt{30}}{3} for x_{2}.

$$9x^{2}+72x-336=9\left(x-\left(\frac{4\sqrt{30}}{3}-4\right)\right)\left(x-\left(-\frac{4\sqrt{30}}{3}-4\right)\right)$$

Evaluate

$$9x^{2}+72x-336$$