Solve Using the Quadratic Formula x^2+18x+65=0

$x^{2} + 18 x + 65 = 0$

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 $a = 1$ , $b = 18$ , and $c = 65$ into the quadratic formula and solve for $x$ .

$\frac{- 18 \pm \sqrt{18^{2} - 4 \cdot (1 \cdot 65)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 18 \pm \sqrt{324 - 4 \cdot 1 \cdot 65}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 65$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 18 \pm \sqrt{324 - 4 \cdot 65}}{2 \cdot 1}$

Multiply $- 4$ by $65$ .

$x = \frac{- 18 \pm \sqrt{324 - 260}}{2 \cdot 1}$

Subtract $260$ from $324$ .

$x = \frac{- 18 \pm \sqrt{64}}{2 \cdot 1}$

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

$x = \frac{- 18 \pm \sqrt{8^{2}}}{2 \cdot 1}$

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

$x = \frac{- 18 \pm 8}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 18 \pm 8}{2}$

Simplify $\frac{- 18 \pm 8}{2}$ .

$x = - 9 \pm 4$

Step 4

The final answer is the combination of both solutions.

$x = - 5, - 13$