Solve Using the Quadratic Formula x^2+10x+35=0

$x^{2} + 10 x + 35 = 0$

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 $a = 1$ , $b = 10$ , and $c = 35$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (1 \cdot 35)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 1 \cdot 35}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 35}}{2 \cdot 1}$

Multiply $- 4$ by $35$ .

$x = \frac{- 10 \pm \sqrt{100 - 140}}{2 \cdot 1}$

Subtract $140$ from $100$ .

$x = \frac{- 10 \pm \sqrt{- 40}}{2 \cdot 1}$

Rewrite $- 40$ as $- 1 (40)$ .

$x = \frac{- 10 \pm \sqrt{- 1 \cdot 40}}{2 \cdot 1}$

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$x = \frac{- 10 \pm \sqrt{- 1} \cdot \sqrt{40}}{2 \cdot 1}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 10 \pm i \cdot \sqrt{40}}{2 \cdot 1}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x = \frac{- 10 \pm i \cdot \sqrt{4 (10)}}{2 \cdot 1}$

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

$x = \frac{- 10 \pm i \cdot \sqrt{2^{2} \cdot 10}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 10 \pm i \cdot (2 \sqrt{10})}{2 \cdot 1}$

Move $2$ to the left of $i$ .

$x = \frac{- 10 \pm 2 i \sqrt{10}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 10 \pm 2 i \sqrt{10}}{2}$

Simplify $\frac{- 10 \pm 2 i \sqrt{10}}{2}$ .

$x = - 5 \pm i \sqrt{10}$