Solve x^2+100x-240000

$${ x }^{ 2 } +100x-240000$$

Factor

$$\left(x-\left(-50\sqrt{97}-50\right)\right)\left(x-\left(50\sqrt{97}-50\right)\right)$$

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.

$$x^{2}+100x-240000=0$$

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.

$$x=\frac{-100±\sqrt{100^{2}-4\left(-240000\right)}}{2}$$

Square 100.

$$x=\frac{-100±\sqrt{10000-4\left(-240000\right)}}{2}$$

Multiply -4 times -240000.

$$x=\frac{-100±\sqrt{10000+960000}}{2}$$

Add 10000 to 960000.

$$x=\frac{-100±\sqrt{970000}}{2}$$

Take the square root of 970000.

$$x=\frac{-100±100\sqrt{97}}{2}$$

Now solve the equation x=\frac{-100±100\sqrt{97}}{2} when ± is plus. Add -100 to 100\sqrt{97}.

$$x=\frac{100\sqrt{97}-100}{2}$$

Divide -100+100\sqrt{97} by 2.

$$x=50\sqrt{97}-50$$

Now solve the equation x=\frac{-100±100\sqrt{97}}{2} when ± is minus. Subtract 100\sqrt{97} from -100.

$$x=\frac{-100\sqrt{97}-100}{2}$$

Divide -100-100\sqrt{97} by 2.

$$x=-50\sqrt{97}-50$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -50+50\sqrt{97} for x_{1} and -50-50\sqrt{97} for x_{2}.

$$x^{2}+100x-240000=\left(x-\left(50\sqrt{97}-50\right)\right)\left(x-\left(-50\sqrt{97}-50\right)\right)$$

Evaluate

$$x^{2}+100x-240000$$