Solve [2]x^2-5x-6

$$[ 2 ] x ^ { 2 } - 5 x - 6$$

Factor

$$2\left(x-\frac{5-\sqrt{73}}{4}\right)\left(x-\frac{\sqrt{73}+5}{4}\right)$$

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.

$$2x^{2}-5x-6=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 2\left(-6\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-5\right)±\sqrt{25-8\left(-6\right)}}{2\times 2}$$

Multiply -8 times -6.

$$x=\frac{-\left(-5\right)±\sqrt{25+48}}{2\times 2}$$

Add 25 to 48.

$$x=\frac{-\left(-5\right)±\sqrt{73}}{2\times 2}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{73}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{5±\sqrt{73}}{4}$$

Now solve the equation x=\frac{5±\sqrt{73}}{4} when ± is plus. Add 5 to \sqrt{73}.

$$x=\frac{\sqrt{73}+5}{4}$$

Now solve the equation x=\frac{5±\sqrt{73}}{4} when ± is minus. Subtract \sqrt{73} from 5.

$$x=\frac{5-\sqrt{73}}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{5+\sqrt{73}}{4} for x_{1} and \frac{5-\sqrt{73}}{4} for x_{2}.

$$2x^{2}-5x-6=2\left(x-\frac{\sqrt{73}+5}{4}\right)\left(x-\frac{5-\sqrt{73}}{4}\right)$$

Evaluate

$$2x^{2}-5x-6$$