Solve 8-2x^2-2x

$$8 - 2 x ^ { 2 } - 2 x$$

Factor

$$-2\left(x-\frac{-\sqrt{17}-1}{2}\right)\left(x-\frac{\sqrt{17}-1}{2}\right)$$

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.

$$-2x^{2}-2x+8=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-2\right)\times 8}}{2\left(-2\right)}$$

Square -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-2\right)\times 8}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{-\left(-2\right)±\sqrt{4+8\times 8}}{2\left(-2\right)}$$

Multiply 8 times 8.

$$x=\frac{-\left(-2\right)±\sqrt{4+64}}{2\left(-2\right)}$$

Add 4 to 64.

$$x=\frac{-\left(-2\right)±\sqrt{68}}{2\left(-2\right)}$$

Take the square root of 68.

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

The opposite of -2 is 2.

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

Multiply 2 times -2.

$$x=\frac{2±2\sqrt{17}}{-4}$$

Now solve the equation x=\frac{2±2\sqrt{17}}{-4} when ± is plus. Add 2 to 2\sqrt{17}.

$$x=\frac{2\sqrt{17}+2}{-4}$$

Divide 2+2\sqrt{17} by -4.

$$x=\frac{-\sqrt{17}-1}{2}$$

Now solve the equation x=\frac{2±2\sqrt{17}}{-4} when ± is minus. Subtract 2\sqrt{17} from 2.

$$x=\frac{2-2\sqrt{17}}{-4}$$

Divide 2-2\sqrt{17} by -4.

$$x=\frac{\sqrt{17}-1}{2}$$

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

$$-2x^{2}-2x+8=-2\left(x-\frac{-\sqrt{17}-1}{2}\right)\left(x-\frac{\sqrt{17}-1}{2}\right)$$

Evaluate

$$8-2x-2x^{2}$$