Solve Using the Quadratic Formula 2-x^2-x=0

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

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = - 1$ , $b = - 1$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (- 1 \cdot 2)}}{2 \cdot - 1}$

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot - 1 \cdot 2}}{2 \cdot - 1}$

Multiply $- 4$ by $- 1$ .

$x = \frac{1 \pm \sqrt{1 + 4 \cdot 2}}{2 \cdot - 1}$

Multiply $4$ by $2$ .

$x = \frac{1 \pm \sqrt{1 + 8}}{2 \cdot - 1}$

Add $1$ and $8$ .

$x = \frac{1 \pm \sqrt{9}}{2 \cdot - 1}$

Rewrite $9$ as $3^{2}$ .

$x = \frac{1 \pm \sqrt{3^{2}}}{2 \cdot - 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{1 \pm 3}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{1 \pm 3}{- 2}$

Move the negative in front of the fraction.

$x = - \frac{1 \pm 3}{2}$

The final answer is the combination of both solutions.

$x = - 2, 1$