Solve x^2-489x+28680

$${ x }^{ 2 } -489x+28680$$

Factor

$$\left(x-\frac{489-\sqrt{124401}}{2}\right)\left(x-\frac{\sqrt{124401}+489}{2}\right)$$

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.

$$x^{2}-489x+28680=0$$

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.

$$x=\frac{-\left(-489\right)±\sqrt{\left(-489\right)^{2}-4\times 28680}}{2}$$

Square -489.

$$x=\frac{-\left(-489\right)±\sqrt{239121-4\times 28680}}{2}$$

Multiply -4 times 28680.

$$x=\frac{-\left(-489\right)±\sqrt{239121-114720}}{2}$$

Add 239121 to -114720.

$$x=\frac{-\left(-489\right)±\sqrt{124401}}{2}$$

The opposite of -489 is 489.

$$x=\frac{489±\sqrt{124401}}{2}$$

Now solve the equation x=\frac{489±\sqrt{124401}}{2} when ± is plus. Add 489 to \sqrt{124401}.

$$x=\frac{\sqrt{124401}+489}{2}$$

Now solve the equation x=\frac{489±\sqrt{124401}}{2} when ± is minus. Subtract \sqrt{124401} from 489.

$$x=\frac{489-\sqrt{124401}}{2}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{489+\sqrt{124401}}{2} for x_{1} and \frac{489-\sqrt{124401}}{2} for x_{2}.

$$x^{2}-489x+28680=\left(x-\frac{\sqrt{124401}+489}{2}\right)\left(x-\frac{489-\sqrt{124401}}{2}\right)$$

Evaluate

$$x^{2}-489x+28680$$