Find the Discriminant 0=x^2+2x+9

$0 = x^{2} + 2 x + 9$

Step 1

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

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

$- x^{2} = 2 x + 9$

Subtract $2 x$ from both sides of the equation.

$- x^{2} - 2 x = 9$

Subtract $9$ from both sides of the equation.

$- x^{2} - 2 x - 9 = 0$

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 $c$ .

${(- 2)}^{2} - 4 (- - 9)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$4 - 4 (- - 9)$

Multiply $- 4 (- - 9)$ .

Multiply $- 1$ by $- 9$ .

$4 - 4 \cdot 9$

Multiply $- 4$ by $9$ .

$4 - 36$

Subtract $36$ from $4$ .

$- 32$