Solve 2x^2-11x-10=

$$2 { x }^{ 2 } -11x-10=$$

Factor

$$2\left(x-\frac{11-\sqrt{201}}{4}\right)\left(x-\frac{\sqrt{201}+11}{4}\right)$$

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.

$$2x^{2}-11x-10=0$$

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.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 2\left(-10\right)}}{2\times 2}$$

Square -11.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\times 2\left(-10\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-11\right)±\sqrt{121-8\left(-10\right)}}{2\times 2}$$

Multiply -8 times -10.

$$x=\frac{-\left(-11\right)±\sqrt{121+80}}{2\times 2}$$

Add 121 to 80.

$$x=\frac{-\left(-11\right)±\sqrt{201}}{2\times 2}$$

The opposite of -11 is 11.

$$x=\frac{11±\sqrt{201}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{11±\sqrt{201}}{4}$$

Now solve the equation x=\frac{11±\sqrt{201}}{4} when ± is plus. Add 11 to \sqrt{201}.

$$x=\frac{\sqrt{201}+11}{4}$$

Now solve the equation x=\frac{11±\sqrt{201}}{4} when ± is minus. Subtract \sqrt{201} from 11.

$$x=\frac{11-\sqrt{201}}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{11+\sqrt{201}}{4} for x_{1} and \frac{11-\sqrt{201}}{4} for x_{2}.

$$2x^{2}-11x-10=2\left(x-\frac{\sqrt{201}+11}{4}\right)\left(x-\frac{11-\sqrt{201}}{4}\right)$$

Evaluate

$$2x^{2}-11x-10$$