Solve -2x^2-4x+2

$$-2 { x }^{ 2 } -4x+2$$

Factor

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

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.

$$-2x^{2}-4x+2=0$$

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.

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

Square -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-2\right)\times 2}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{-\left(-4\right)±\sqrt{16+8\times 2}}{2\left(-2\right)}$$

Multiply 8 times 2.

$$x=\frac{-\left(-4\right)±\sqrt{16+16}}{2\left(-2\right)}$$

Add 16 to 16.

$$x=\frac{-\left(-4\right)±\sqrt{32}}{2\left(-2\right)}$$

Take the square root of 32.

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

The opposite of -4 is 4.

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

Multiply 2 times -2.

$$x=\frac{4±4\sqrt{2}}{-4}$$

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

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

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

$$x=-\left(\sqrt{2}+1\right)$$

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

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

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

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

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

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

Evaluate

$$2-4x-2x^{2}$$