Solve x^2+30x-120

$${ x }^{ 2 } +30x-120$$

Factor

$$\left(x-\left(-\sqrt{345}-15\right)\right)\left(x-\left(\sqrt{345}-15\right)\right)$$

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.

$$x^{2}+30x-120=0$$

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.

$$x=\frac{-30±\sqrt{30^{2}-4\left(-120\right)}}{2}$$

Square 30.

$$x=\frac{-30±\sqrt{900-4\left(-120\right)}}{2}$$

Multiply -4 times -120.

$$x=\frac{-30±\sqrt{900+480}}{2}$$

Add 900 to 480.

$$x=\frac{-30±\sqrt{1380}}{2}$$

Take the square root of 1380.

$$x=\frac{-30±2\sqrt{345}}{2}$$

Now solve the equation x=\frac{-30±2\sqrt{345}}{2} when ± is plus. Add -30 to 2\sqrt{345}.

$$x=\frac{2\sqrt{345}-30}{2}$$

Divide -30+2\sqrt{345} by 2.

$$x=\sqrt{345}-15$$

Now solve the equation x=\frac{-30±2\sqrt{345}}{2} when ± is minus. Subtract 2\sqrt{345} from -30.

$$x=\frac{-2\sqrt{345}-30}{2}$$

Divide -30-2\sqrt{345} by 2.

$$x=-\sqrt{345}-15$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -15+\sqrt{345} for x_{1} and -15-\sqrt{345} for x_{2}.

$$x^{2}+30x-120=\left(x-\left(\sqrt{345}-15\right)\right)\left(x-\left(-\sqrt{345}-15\right)\right)$$

Evaluate

$$x^{2}+30x-120$$