Solve -1-5x-2x^2

$$- 1 - 5 x - 2 x ^ { 2 }$$

Factor

$$-2\left(x-\frac{-\sqrt{17}-5}{4}\right)\left(x-\frac{\sqrt{17}-5}{4}\right)$$

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.

$$-2x^{2}-5x-1=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-2\right)\left(-1\right)}}{2\left(-2\right)}$$

Square -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-2\right)\left(-1\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{-\left(-5\right)±\sqrt{25+8\left(-1\right)}}{2\left(-2\right)}$$

Multiply 8 times -1.

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

Add 25 to -8.

$$x=\frac{-\left(-5\right)±\sqrt{17}}{2\left(-2\right)}$$

The opposite of -5 is 5.

$$x=\frac{5±\sqrt{17}}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{5±\sqrt{17}}{-4}$$

Now solve the equation x=\frac{5±\sqrt{17}}{-4} when ± is plus. Add 5 to \sqrt{17}.

$$x=\frac{\sqrt{17}+5}{-4}$$

Divide 5+\sqrt{17} by -4.

$$x=\frac{-\sqrt{17}-5}{4}$$

Now solve the equation x=\frac{5±\sqrt{17}}{-4} when ± is minus. Subtract \sqrt{17} from 5.

$$x=\frac{5-\sqrt{17}}{-4}$$

Divide 5-\sqrt{17} by -4.

$$x=\frac{\sqrt{17}-5}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5-\sqrt{17}}{4} for x_{1} and \frac{-5+\sqrt{17}}{4} for x_{2}.

$$-2x^{2}-5x-1=-2\left(x-\frac{-\sqrt{17}-5}{4}\right)\left(x-\frac{\sqrt{17}-5}{4}\right)$$

Evaluate

$$-2x^{2}-5x-1$$