Solve -2x^2-2x-2

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

Factor

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

Solution Steps

Factor out 2. Polynomial -x^{2}-x-1 is not factored since it does not have any rational roots.

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

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.

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

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.

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

Square -2.

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

Multiply -4 times -2.

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

Multiply 8 times -2.

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

Add 4 to -16.

$$x=\frac{-\left(-2\right)±\sqrt{-12}}{2\left(-2\right)}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Quadratic polynomial cannot be factored.

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

Evaluate

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