Solve x^2-315x+120

$${ x }^{ 2 } -315x+120$$

Factor

$$\left(x-\frac{315-\sqrt{98745}}{2}\right)\left(x-\frac{\sqrt{98745}+315}{2}\right)$$

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.

$$x^{2}-315x+120=0$$

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.

$$x=\frac{-\left(-315\right)±\sqrt{\left(-315\right)^{2}-4\times 120}}{2}$$

Square -315.

$$x=\frac{-\left(-315\right)±\sqrt{99225-4\times 120}}{2}$$

Multiply -4 times 120.

$$x=\frac{-\left(-315\right)±\sqrt{99225-480}}{2}$$

Add 99225 to -480.

$$x=\frac{-\left(-315\right)±\sqrt{98745}}{2}$$

The opposite of -315 is 315.

$$x=\frac{315±\sqrt{98745}}{2}$$

Now solve the equation x=\frac{315±\sqrt{98745}}{2} when ± is plus. Add 315 to \sqrt{98745}.

$$x=\frac{\sqrt{98745}+315}{2}$$

Now solve the equation x=\frac{315±\sqrt{98745}}{2} when ± is minus. Subtract \sqrt{98745} from 315.

$$x=\frac{315-\sqrt{98745}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{315+\sqrt{98745}}{2} for x_{1} and \frac{315-\sqrt{98745}}{2} for x_{2}.

$$x^{2}-315x+120=\left(x-\frac{\sqrt{98745}+315}{2}\right)\left(x-\frac{315-\sqrt{98745}}{2}\right)$$

Evaluate

$$x^{2}-315x+120$$