Solve Using the Quadratic Formula c^2+10c+9=0

$c^{2} + 10 c + 9 = 0$

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 $a = 1$ , $b = 10$ , and $c = 9$ into the quadratic formula and solve for $c$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (1 \cdot 9)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$c = \frac{- 10 \pm \sqrt{100 - 4 \cdot 1 \cdot 9}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 9$ .

Multiply $- 4$ by $1$ .

$c = \frac{- 10 \pm \sqrt{100 - 4 \cdot 9}}{2 \cdot 1}$

Multiply $- 4$ by $9$ .

$c = \frac{- 10 \pm \sqrt{100 - 36}}{2 \cdot 1}$

Subtract $36$ from $100$ .

$c = \frac{- 10 \pm \sqrt{64}}{2 \cdot 1}$

Rewrite $64$ as $8^{2}$ .

$c = \frac{- 10 \pm \sqrt{8^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$c = \frac{- 10 \pm 8}{2 \cdot 1}$

Multiply $2$ by $1$ .

$c = \frac{- 10 \pm 8}{2}$

Simplify $\frac{- 10 \pm 8}{2}$ .

$c = - 5 \pm 4$

Step 4

The final answer is the combination of both solutions.

$c = - 1, - 9$