Find the Discriminant 2x^2=-2x-1

$2 x^{2} = - 2 x - 1$

Step 1

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

Add $2 x$ to both sides of the equation.

$2 x^{2} + 2 x = - 1$

Add $1$ to both sides of the equation.

$2 x^{2} + 2 x + 1 = 0$

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 $c$ .

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

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$4 - 4 (2 \cdot 1)$

Multiply $- 4 (2 \cdot 1)$ .

Multiply $2$ by $1$ .

$4 - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$4 - 8$

Subtract $8$ from $4$ .

$- 4$