Find the Discriminant -x^2+2x+66=-2x^2+1

$- x^{2} + 2 x + 66 = - 2 x^{2} + 1$

Move all terms to the left side of the equation and simplify.

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

Add $2 x^{2}$ to both sides of the equation.

$- x^{2} + 2 x + 66 + 2 x^{2} = 1$

Subtract $1$ from both sides of the equation.

$- x^{2} + 2 x + 66 + 2 x^{2} - 1 = 0$

Simplify $- x^{2} + 2 x + 66 + 2 x^{2} - 1$ .

Add $- x^{2}$ and $2 x^{2}$ .

$x^{2} + 2 x + 66 - 1 = 0$

Subtract $1$ from $66$ .

$x^{2} + 2 x + 65 = 0$

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

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

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

$2^{2} - 4 (1 \cdot 65)$

Evaluate the result to find the discriminant.

Simplify each term.

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

$4 - 4 (1 \cdot 65)$

Multiply $65$ by $1$ .

$4 - 4 \cdot 65$

Multiply $- 4$ by $65$ .

$4 - 260$

Subtract $260$ from $4$ .

$- 256$