Find the Discriminant 10x+y=-x^2+2

$10 x + y = - x^{2} + 2$

Subtract $10 x$ from both sides of the equation.

$y = - x^{2} + 2 - 10 x$

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 $c$ .

${(- 10)}^{2} - 4 (- 1 \cdot 2)$

Evaluate the result to find the discriminant.

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Simplify each term.

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Raise $- 10$ to the power of $2$ .

$100 - 4 (- 1 \cdot 2)$

Multiply $- 1$ by $2$ .

$100 - 4 \cdot - 2$

Multiply $- 4$ by $- 2$ .

$100 + 8$

Add $100$ and $8$ .

$108$

Find the Discriminant 10x+y=-x^2+2

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