Solve Using the Quadratic Formula 2x^2+40=0

$2 x^{2} + 40 = 0$

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 $a = 2$ , $b = 0$ , and $c = 40$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot 40)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot 40}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 40$ .

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot 40}}{2 \cdot 2}$

Multiply $- 8$ by $40$ .

$x = \frac{0 \pm \sqrt{0 - 320}}{2 \cdot 2}$

Subtract $320$ from $0$ .

$x = \frac{0 \pm \sqrt{- 320}}{2 \cdot 2}$

Rewrite $- 320$ as $- 1 (320)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 320}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (320)}$ as $\sqrt{- 1} \cdot \sqrt{320}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{320}}{2 \cdot 2}$

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

$x = \frac{0 \pm i \cdot \sqrt{320}}{2 \cdot 2}$

Rewrite $320$ as $8^{2} \cdot 5$ .

Factor $64$ out of $320$ .

$x = \frac{0 \pm i \cdot \sqrt{64 (5)}}{2 \cdot 2}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{8^{2} \cdot 5}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (8 \sqrt{5})}{2 \cdot 2}$

Move $8$ to the left of $i$ .

$x = \frac{0 \pm 8 i \sqrt{5}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{0 \pm 8 i \sqrt{5}}{4}$

Simplify $\frac{0 \pm 8 i \sqrt{5}}{4}$ .

$x = \pm 2 i \sqrt{5}$