Solve Using the Quadratic Formula x^2+19x+c=0

$x^{2} + 19 x + c = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 1$ , $b = 19$ , and $c = c$ into the quadratic formula and solve for $x$ .

$\frac{- 19 \pm \sqrt{19^{2} - 4 \cdot (1 \cdot c)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $19$ to the power of $2$ .

$x = \frac{- 19 \pm \sqrt{361 - 4 \cdot 1 \cdot c}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 19 \pm \sqrt{361 - 4 c}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 19 \pm \sqrt{361 - 4 c}}{2}$