Algebra Examples

$2 x^{2} + 50 = 0$

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 $c = 50$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot 50)}}{2 \cdot 2}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot 50}}{2 \cdot 2}$

Step 3.1.2

Multiply $- 4 \cdot 2 \cdot 50$ .

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Step 3.1.2.1

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot 50}}{2 \cdot 2}$

Step 3.1.2.2

Multiply $- 8$ by $50$ .

$x = \frac{0 \pm \sqrt{0 - 400}}{2 \cdot 2}$

Step 3.1.3

Subtract $400$ from $0$ .

$x = \frac{0 \pm \sqrt{- 400}}{2 \cdot 2}$

Step 3.1.4

Rewrite $- 400$ as $- 1 (400)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 400}}{2 \cdot 2}$

Step 3.1.5

Rewrite $\sqrt{- 1 (400)}$ as $\sqrt{- 1} \cdot \sqrt{400}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{400}}{2 \cdot 2}$

Step 3.1.6

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

$x = \frac{0 \pm i \cdot \sqrt{400}}{2 \cdot 2}$

Step 3.1.7

Rewrite $400$ as $20^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{20^{2}}}{2 \cdot 2}$

Step 3.1.8

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm i \cdot 20}{2 \cdot 2}$

Step 3.1.9

Move $20$ to the left of $i$ .

$x = \frac{0 \pm 20 i}{2 \cdot 2}$

Step 3.2

Multiply $2$ by $2$ .

$x = \frac{0 \pm 20 i}{4}$

Step 3.3

Simplify $\frac{0 \pm 20 i}{4}$ .

$x = \pm 5 i$