Solve -2x^2-2x

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

Factor

$$-2x\left(x+1\right)$$

Solution Steps

Factor out 2.

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

Consider -x^{2}-x. Factor out x.

$$x\left(-x-1\right)$$

Rewrite the complete factored expression.

$$2x\left(-x-1\right)$$

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.

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

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.

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

Take the square root of \left(-2\right)^{2}.

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

The opposite of -2 is 2.

$$x=\frac{2±2}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{2±2}{-4}$$

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

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

Divide 4 by -4.

$$x=-1$$

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

$$x=\frac{0}{-4}$$

Divide 0 by -4.

$$x=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -1 for x_{1} and 0 for x_{2}.

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

Simplify all the expressions of the form p-\left(-q\right) to p+q.

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

Evaluate

$$-2x\left(x+1\right)$$