Find the Discriminant 0=x+2+x^2

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

Step 1

Move all the expressions to the left side of the equation.

Subtract $x$ from both sides of the equation.

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

Subtract $2$ from both sides of the equation.

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

Subtract $x^{2}$ from both sides of the equation.

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

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 1)}^{2} - 4 (- - 2)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$1 - 4 (- - 2)$

Multiply $- 4 (- - 2)$ .

Multiply $- 1$ by $- 2$ .

$1 - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$1 - 8$

Subtract $8$ from $1$ .

$- 7$