Algebra Examples

$x^{2} = - 16$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 16}$

Step 2

Simplify

$\pm \sqrt{- 16}$ .

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Step 2.1

Rewrite

$- 16$ as

$- 1 (16)$ .

$x = \pm \sqrt{- 1 (16)}$

Step 2.2

Rewrite

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

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

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

Step 2.3

Rewrite

$\sqrt{- 1}$ as

$i$ .

$x = \pm i \cdot \sqrt{16}$

Step 2.4

Rewrite

$16$ as

$4^{2}$ .

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

Step 2.5

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

$x = \pm i \cdot 4$

Step 2.6

Move

$4$ to the left of

$i$ .

$x = \pm 4 i$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the

$\pm$ to find the first solution.

$x = 4 i$

Step 3.2

Next, use the negative value of the

$\pm$ to find the second solution.

$x = - 4 i$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 4 i, - 4 i$

$x^{2} = - 16$

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