Solve x^2+30x-200

$${ x }^{ 2 } +30x-200$$

Factor

$$\left(x-\left(-5\sqrt{17}-15\right)\right)\left(x-\left(5\sqrt{17}-15\right)\right)$$

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.

$$x^{2}+30x-200=0$$

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.

$$x=\frac{-30±\sqrt{30^{2}-4\left(-200\right)}}{2}$$

Square 30.

$$x=\frac{-30±\sqrt{900-4\left(-200\right)}}{2}$$

Multiply -4 times -200.

$$x=\frac{-30±\sqrt{900+800}}{2}$$

Add 900 to 800.

$$x=\frac{-30±\sqrt{1700}}{2}$$

Take the square root of 1700.

$$x=\frac{-30±10\sqrt{17}}{2}$$

Now solve the equation x=\frac{-30±10\sqrt{17}}{2} when ± is plus. Add -30 to 10\sqrt{17}.

$$x=\frac{10\sqrt{17}-30}{2}$$

Divide -30+10\sqrt{17} by 2.

$$x=5\sqrt{17}-15$$

Now solve the equation x=\frac{-30±10\sqrt{17}}{2} when ± is minus. Subtract 10\sqrt{17} from -30.

$$x=\frac{-10\sqrt{17}-30}{2}$$

Divide -30-10\sqrt{17} by 2.

$$x=-5\sqrt{17}-15$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -15+5\sqrt{17} for x_{1} and -15-5\sqrt{17} for x_{2}.

$$x^{2}+30x-200=\left(x-\left(5\sqrt{17}-15\right)\right)\left(x-\left(-5\sqrt{17}-15\right)\right)$$

Evaluate

$$x^{2}+30x-200$$