Solve 2x^2-17x-24=

$$2 { x }^{ 2 } -17x-24=$$

Factor

$$2\left(x-\frac{17-\sqrt{481}}{4}\right)\left(x-\frac{\sqrt{481}+17}{4}\right)$$

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.

$$2x^{2}-17x-24=0$$

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.

$$x=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Square -17.

$$x=\frac{-\left(-17\right)±\sqrt{289-4\times 2\left(-24\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-17\right)±\sqrt{289-8\left(-24\right)}}{2\times 2}$$

Multiply -8 times -24.

$$x=\frac{-\left(-17\right)±\sqrt{289+192}}{2\times 2}$$

Add 289 to 192.

$$x=\frac{-\left(-17\right)±\sqrt{481}}{2\times 2}$$

The opposite of -17 is 17.

$$x=\frac{17±\sqrt{481}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{17±\sqrt{481}}{4}$$

Now solve the equation x=\frac{17±\sqrt{481}}{4} when ± is plus. Add 17 to \sqrt{481}.

$$x=\frac{\sqrt{481}+17}{4}$$

Now solve the equation x=\frac{17±\sqrt{481}}{4} when ± is minus. Subtract \sqrt{481} from 17.

$$x=\frac{17-\sqrt{481}}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{17+\sqrt{481}}{4} for x_{1} and \frac{17-\sqrt{481}}{4} for x_{2}.

$$2x^{2}-17x-24=2\left(x-\frac{\sqrt{481}+17}{4}\right)\left(x-\frac{17-\sqrt{481}}{4}\right)$$

Evaluate

$$2x^{2}-17x-24$$