Solve 0-x-x^2

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

Factor

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

Solution Steps

Factor out x.

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

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.

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

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.

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

Take the square root of 1.

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

The opposite of -1 is 1.

$$x=\frac{1±1}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{1±1}{-2}$$

Now solve the equation x=\frac{1±1}{-2} when ± is plus. Add 1 to 1.

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

Divide 2 by -2.

$$x=-1$$

Now solve the equation x=\frac{1±1}{-2} when ± is minus. Subtract 1 from 1.

$$x=\frac{0}{-2}$$

Divide 0 by -2.

$$x=0$$

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}.

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

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

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

Evaluate

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

Solution Steps

Anything plus zero gives itself.

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