Solve Using the Quadratic Formula x^2+14x+35=0

$x^{2} + 14 x + 35 = 0$

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 $c = 35$ into the quadratic formula and solve for $x$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (1 \cdot 35)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 1 \cdot 35}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 35$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 35}}{2 \cdot 1}$

Multiply $- 4$ by $35$ .

$x = \frac{- 14 \pm \sqrt{196 - 140}}{2 \cdot 1}$

Subtract $140$ from $196$ .

$x = \frac{- 14 \pm \sqrt{56}}{2 \cdot 1}$

Rewrite $56$ as $2^{2} \cdot 14$ .

Factor $4$ out of $56$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $1$ .

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

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

$x = - 7 \pm \sqrt{14}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 7 \pm \sqrt{14}$

Decimal Form:

$x = - 3.25834261 \dots, - 10.74165738 \dots$