Solve Using the Quadratic Formula 5n^2+35=0

$5 n^{2} + 35 = 0$

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 $a = 5$ , $b = 0$ , and $c = 35$ into the quadratic formula and solve for $n$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (5 \cdot 35)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$n = \frac{0 \pm \sqrt{0 - 4 \cdot 5 \cdot 35}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 35$ .

Multiply $- 4$ by $5$ .

$n = \frac{0 \pm \sqrt{0 - 20 \cdot 35}}{2 \cdot 5}$

Multiply $- 20$ by $35$ .

$n = \frac{0 \pm \sqrt{0 - 700}}{2 \cdot 5}$

Subtract $700$ from $0$ .

$n = \frac{0 \pm \sqrt{- 700}}{2 \cdot 5}$

Rewrite $- 700$ as $- 1 (700)$ .

$n = \frac{0 \pm \sqrt{- 1 \cdot 700}}{2 \cdot 5}$

Rewrite $\sqrt{- 1 (700)}$ as $\sqrt{- 1} \cdot \sqrt{700}$ .

$n = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{700}}{2 \cdot 5}$

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

$n = \frac{0 \pm i \cdot \sqrt{700}}{2 \cdot 5}$

Rewrite $700$ as $10^{2} \cdot 7$ .

Factor $100$ out of $700$ .

$n = \frac{0 \pm i \cdot \sqrt{100 (7)}}{2 \cdot 5}$

Rewrite $100$ as $10^{2}$ .

$n = \frac{0 \pm i \cdot \sqrt{10^{2} \cdot 7}}{2 \cdot 5}$

Pull terms out from under the radical.

$n = \frac{0 \pm i \cdot (10 \sqrt{7})}{2 \cdot 5}$

Move $10$ to the left of $i$ .

$n = \frac{0 \pm 10 i \sqrt{7}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$n = \frac{0 \pm 10 i \sqrt{7}}{10}$

Simplify $\frac{0 \pm 10 i \sqrt{7}}{10}$ .

$n = \pm i \sqrt{7}$