Solve Using the Quadratic Formula x^2+12x+14=0

$x^{2} + 12 x + 14 = 0$

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 $a = 1$ , $b = 12$ , and $c = 14$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (1 \cdot 14)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 1 \cdot 14}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 14$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 14}}{2 \cdot 1}$

Multiply $- 4$ by $14$ .

$x = \frac{- 12 \pm \sqrt{144 - 56}}{2 \cdot 1}$

Subtract $56$ from $144$ .

$x = \frac{- 12 \pm \sqrt{88}}{2 \cdot 1}$

Rewrite $88$ as $2^{2} \cdot 22$ .

Factor $4$ out of $88$ .

$x = \frac{- 12 \pm \sqrt{4 (22)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 12 \pm \sqrt{2^{2} \cdot 22}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 2 \sqrt{22}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 12 \pm 2 \sqrt{22}}{2}$

Simplify $\frac{- 12 \pm 2 \sqrt{22}}{2}$ .

$x = - 6 \pm \sqrt{22}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 6 \pm \sqrt{22}$

Decimal Form:

$x = - 1.30958424 \dots, - 10.69041575 \dots$