Solve x^2-200x-2400

$${ x }^{ 2 } -200x-2400$$

Factor

$$\left(x-\left(100-20\sqrt{31}\right)\right)\left(x-\left(20\sqrt{31}+100\right)\right)$$

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.

$$x^{2}-200x-2400=0$$

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.

$$x=\frac{-\left(-200\right)±\sqrt{\left(-200\right)^{2}-4\left(-2400\right)}}{2}$$

Square -200.

$$x=\frac{-\left(-200\right)±\sqrt{40000-4\left(-2400\right)}}{2}$$

Multiply -4 times -2400.

$$x=\frac{-\left(-200\right)±\sqrt{40000+9600}}{2}$$

Add 40000 to 9600.

$$x=\frac{-\left(-200\right)±\sqrt{49600}}{2}$$

Take the square root of 49600.

$$x=\frac{-\left(-200\right)±40\sqrt{31}}{2}$$

The opposite of -200 is 200.

$$x=\frac{200±40\sqrt{31}}{2}$$

Now solve the equation x=\frac{200±40\sqrt{31}}{2} when ± is plus. Add 200 to 40\sqrt{31}.

$$x=\frac{40\sqrt{31}+200}{2}$$

Divide 200+40\sqrt{31} by 2.

$$x=20\sqrt{31}+100$$

Now solve the equation x=\frac{200±40\sqrt{31}}{2} when ± is minus. Subtract 40\sqrt{31} from 200.

$$x=\frac{200-40\sqrt{31}}{2}$$

Divide 200-40\sqrt{31} by 2.

$$x=100-20\sqrt{31}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 100+20\sqrt{31} for x_{1} and 100-20\sqrt{31} for x_{2}.

$$x^{2}-200x-2400=\left(x-\left(20\sqrt{31}+100\right)\right)\left(x-\left(100-20\sqrt{31}\right)\right)$$

Evaluate

$$x^{2}-200x-2400$$