Solve x^2-114514x-1919810

$${ x }^{ 2 } -114514x-1919810$$

Factor

$$\left(x-\left(57257-\sqrt{3280283859}\right)\right)\left(x-\left(\sqrt{3280283859}+57257\right)\right)$$

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.

$$x^{2}-114514x-1919810=0$$

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.

$$x=\frac{-\left(-114514\right)±\sqrt{\left(-114514\right)^{2}-4\left(-1919810\right)}}{2}$$

Square -114514.

$$x=\frac{-\left(-114514\right)±\sqrt{13113456196-4\left(-1919810\right)}}{2}$$

Multiply -4 times -1919810.

$$x=\frac{-\left(-114514\right)±\sqrt{13113456196+7679240}}{2}$$

Add 13113456196 to 7679240.

$$x=\frac{-\left(-114514\right)±\sqrt{13121135436}}{2}$$

Take the square root of 13121135436.

$$x=\frac{-\left(-114514\right)±2\sqrt{3280283859}}{2}$$

The opposite of -114514 is 114514.

$$x=\frac{114514±2\sqrt{3280283859}}{2}$$

Now solve the equation x=\frac{114514±2\sqrt{3280283859}}{2} when ± is plus. Add 114514 to 2\sqrt{3280283859}.

$$x=\frac{2\sqrt{3280283859}+114514}{2}$$

Divide 114514+2\sqrt{3280283859} by 2.

$$x=\sqrt{3280283859}+57257$$

Now solve the equation x=\frac{114514±2\sqrt{3280283859}}{2} when ± is minus. Subtract 2\sqrt{3280283859} from 114514.

$$x=\frac{114514-2\sqrt{3280283859}}{2}$$

Divide 114514-2\sqrt{3280283859} by 2.

$$x=57257-\sqrt{3280283859}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 57257+\sqrt{3280283859} for x_{1} and 57257-\sqrt{3280283859} for x_{2}.

$$x^{2}-114514x-1919810=\left(x-\left(\sqrt{3280283859}+57257\right)\right)\left(x-\left(57257-\sqrt{3280283859}\right)\right)$$

Evaluate

$$x^{2}-114514x-1919810$$