Algebra Examples

$x^{2} + 81 = 0$

Step 1

Subtract $81$ from both sides of the equation.

$x^{2} = - 81$

Step 2

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

$x = \pm \sqrt{- 81}$

Step 3

Simplify $\pm \sqrt{- 81}$ .

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Step 3.1

Rewrite $- 81$ as $- 1 (81)$ .

$x = \pm \sqrt{- 1 (81)}$

Step 3.2

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{81}$

Step 3.3

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

$x = \pm i \cdot \sqrt{81}$

Step 3.4

Rewrite $81$ as $9^{2}$ .

$x = \pm i \cdot \sqrt{9^{2}}$

Step 3.5

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

$x = \pm i \cdot 9$

Step 3.6

Move $9$ to the left of $i$ .

$x = \pm 9 i$

Step 4

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

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 9 i$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 9 i$

Step 4.3

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

$x = 9 i, - 9 i$