Solve x^2+1270x-80645

$${ x }^{ 2 } +1270x-80645$$

Factor

$$\left(x-\left(-127\sqrt{30}-635\right)\right)\left(x-\left(127\sqrt{30}-635\right)\right)$$

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.

$$x^{2}+1270x-80645=0$$

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.

$$x=\frac{-1270±\sqrt{1270^{2}-4\left(-80645\right)}}{2}$$

Square 1270.

$$x=\frac{-1270±\sqrt{1612900-4\left(-80645\right)}}{2}$$

Multiply -4 times -80645.

$$x=\frac{-1270±\sqrt{1612900+322580}}{2}$$

Add 1612900 to 322580.

$$x=\frac{-1270±\sqrt{1935480}}{2}$$

Take the square root of 1935480.

$$x=\frac{-1270±254\sqrt{30}}{2}$$

Now solve the equation x=\frac{-1270±254\sqrt{30}}{2} when ± is plus. Add -1270 to 254\sqrt{30}.

$$x=\frac{254\sqrt{30}-1270}{2}$$

Divide -1270+254\sqrt{30} by 2.

$$x=127\sqrt{30}-635$$

Now solve the equation x=\frac{-1270±254\sqrt{30}}{2} when ± is minus. Subtract 254\sqrt{30} from -1270.

$$x=\frac{-254\sqrt{30}-1270}{2}$$

Divide -1270-254\sqrt{30} by 2.

$$x=-127\sqrt{30}-635$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -635+127\sqrt{30} for x_{1} and -635-127\sqrt{30} for x_{2}.

$$x^{2}+1270x-80645=\left(x-\left(127\sqrt{30}-635\right)\right)\left(x-\left(-127\sqrt{30}-635\right)\right)$$

Evaluate

$$x^{2}+1270x-80645$$