Solve 9x^2+144x-63

$$9 { x }^{ 2 } +144x-63$$

Factor

$$9\left(x-\left(-\sqrt{71}-8\right)\right)\left(x-\left(\sqrt{71}-8\right)\right)$$

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.

$$9x^{2}+144x-63=0$$

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.

$$x=\frac{-144±\sqrt{144^{2}-4\times 9\left(-63\right)}}{2\times 9}$$

Square 144.

$$x=\frac{-144±\sqrt{20736-4\times 9\left(-63\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{-144±\sqrt{20736-36\left(-63\right)}}{2\times 9}$$

Multiply -36 times -63.

$$x=\frac{-144±\sqrt{20736+2268}}{2\times 9}$$

Add 20736 to 2268.

$$x=\frac{-144±\sqrt{23004}}{2\times 9}$$

Take the square root of 23004.

$$x=\frac{-144±18\sqrt{71}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{-144±18\sqrt{71}}{18}$$

Now solve the equation x=\frac{-144±18\sqrt{71}}{18} when ± is plus. Add -144 to 18\sqrt{71}.

$$x=\frac{18\sqrt{71}-144}{18}$$

Divide -144+18\sqrt{71} by 18.

$$x=\sqrt{71}-8$$

Now solve the equation x=\frac{-144±18\sqrt{71}}{18} when ± is minus. Subtract 18\sqrt{71} from -144.

$$x=\frac{-18\sqrt{71}-144}{18}$$

Divide -144-18\sqrt{71} by 18.

$$x=-\sqrt{71}-8$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -8+\sqrt{71} for x_{1} and -8-\sqrt{71} for x_{2}.

$$9x^{2}+144x-63=9\left(x-\left(\sqrt{71}-8\right)\right)\left(x-\left(-\sqrt{71}-8\right)\right)$$

Evaluate

$$9\left(x^{2}+16x-7\right)$$