Find the Discriminant x^2-25x+104=-7x-3

$x^{2} - 25 x + 104 = - 7 x - 3$

Step 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 $7 x$ to both sides of the equation.

$x^{2} - 25 x + 104 + 7 x = - 3$

Add $3$ to both sides of the equation.

$x^{2} - 25 x + 104 + 7 x + 3 = 0$

Simplify $x^{2} - 25 x + 104 + 7 x + 3$ .

Add $- 25 x$ and $7 x$ .

$x^{2} - 18 x + 104 + 3 = 0$

Add $104$ and $3$ .

$x^{2} - 18 x + 107 = 0$

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 $c$ .

${(- 18)}^{2} - 4 (1 \cdot 107)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 18$ to the power of $2$ .

$324 - 4 (1 \cdot 107)$

Multiply $- 4 (1 \cdot 107)$ .

Multiply $107$ by $1$ .

$324 - 4 \cdot 107$

Multiply $- 4$ by $107$ .

$324 - 428$

Subtract $428$ from $324$ .

$- 104$