Algebra Examples

$x^{2} + 4 = 0$

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

$a = 1$ ,

$b = 0$ , and

$c = 4$ into the quadratic formula and solve for

$x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot 4)}}{2 \cdot 1}$

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

$0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot 4}}{2 \cdot 1}$

Step 3.1.2

Multiply

$- 4 \cdot 1 \cdot 4$ .

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Step 3.1.2.1

Multiply

$- 4$ by

$1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 4}}{2 \cdot 1}$

Step 3.1.2.2

Multiply

$- 4$ by

$4$ .

$x = \frac{0 \pm \sqrt{0 - 16}}{2 \cdot 1}$

Step 3.1.3

Subtract

$16$ from

$0$ .

$x = \frac{0 \pm \sqrt{- 16}}{2 \cdot 1}$

Step 3.1.4

Rewrite

$- 16$ as

$- 1 (16)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 16}}{2 \cdot 1}$

Step 3.1.5

Rewrite

$\sqrt{- 1 (16)}$ as

$\sqrt{- 1} \cdot \sqrt{16}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{16}}{2 \cdot 1}$

Step 3.1.6

Rewrite

$\sqrt{- 1}$ as

$i$ .

$x = \frac{0 \pm i \cdot \sqrt{16}}{2 \cdot 1}$

Step 3.1.7

Rewrite

$16$ as

$4^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{4^{2}}}{2 \cdot 1}$

Step 3.1.8

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

$x = \frac{0 \pm i \cdot 4}{2 \cdot 1}$

Step 3.1.9

Move

$4$ to the left of

$i$ .

$x = \frac{0 \pm 4 i}{2 \cdot 1}$

Step 3.2

Multiply

$2$ by

$1$ .

$x = \frac{0 \pm 4 i}{2}$

Step 3.3

Simplify

$\frac{0 \pm 4 i}{2}$ .

$x = \pm 2 i$