Solve Using the Quadratic Formula x^2+14x+26=0

$x^{2} + 14 x + 26 = 0$

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 $a = 1$ , $b = 14$ , and $c = 26$ into the quadratic formula and solve for $x$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (1 \cdot 26)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $14$ to the power of $2$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 1 \cdot 26}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 26$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 26}}{2 \cdot 1}$

Multiply $- 4$ by $26$ .

$x = \frac{- 14 \pm \sqrt{196 - 104}}{2 \cdot 1}$

Subtract $104$ from $196$ .

$x = \frac{- 14 \pm \sqrt{92}}{2 \cdot 1}$

Rewrite $92$ as $2^{2} \cdot 23$ .

Factor $4$ out of $92$ .

$x = \frac{- 14 \pm \sqrt{4 (23)}}{2 \cdot 1}$

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

$x = \frac{- 14 \pm \sqrt{2^{2} \cdot 23}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 14 \pm 2 \sqrt{23}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 14 \pm 2 \sqrt{23}}{2}$

Simplify $\frac{- 14 \pm 2 \sqrt{23}}{2}$ .

$x = - 7 \pm \sqrt{23}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 7 \pm \sqrt{23}$

Decimal Form:

$x = - 2.20416847 \dots, - 11.79583152 \dots$