Solve 60x^2-30x-200

$$60 { x }^{ 2 } -30x-200$$

Factor

$$60\left(x-\left(-\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)\left(x-\left(\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)$$

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.

$$60x^{2}-30x-200=0$$

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.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}-4\times 60\left(-200\right)}}{2\times 60}$$

Square -30.

$$x=\frac{-\left(-30\right)±\sqrt{900-4\times 60\left(-200\right)}}{2\times 60}$$

Multiply -4 times 60.

$$x=\frac{-\left(-30\right)±\sqrt{900-240\left(-200\right)}}{2\times 60}$$

Multiply -240 times -200.

$$x=\frac{-\left(-30\right)±\sqrt{900+48000}}{2\times 60}$$

Add 900 to 48000.

$$x=\frac{-\left(-30\right)±\sqrt{48900}}{2\times 60}$$

Take the square root of 48900.

$$x=\frac{-\left(-30\right)±10\sqrt{489}}{2\times 60}$$

The opposite of -30 is 30.

$$x=\frac{30±10\sqrt{489}}{2\times 60}$$

Multiply 2 times 60.

$$x=\frac{30±10\sqrt{489}}{120}$$

Now solve the equation x=\frac{30±10\sqrt{489}}{120} when ± is plus. Add 30 to 10\sqrt{489}.

$$x=\frac{10\sqrt{489}+30}{120}$$

Divide 30+10\sqrt{489} by 120.

$$x=\frac{\sqrt{489}}{12}+\frac{1}{4}$$

Now solve the equation x=\frac{30±10\sqrt{489}}{120} when ± is minus. Subtract 10\sqrt{489} from 30.

$$x=\frac{30-10\sqrt{489}}{120}$$

Divide 30-10\sqrt{489} by 120.

$$x=-\frac{\sqrt{489}}{12}+\frac{1}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{4}+\frac{\sqrt{489}}{12} for x_{1} and \frac{1}{4}-\frac{\sqrt{489}}{12} for x_{2}.

$$60x^{2}-30x-200=60\left(x-\left(\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)\left(x-\left(-\frac{\sqrt{489}}{12}+\frac{1}{4}\right)\right)$$

Evaluate

$$60x^{2}-30x-200$$