Pre-Algebra Examples

$x^{2} + 25 = 0$

Step 1

Subtract $25$ from both sides of the equation.

$x^{2} = - 25$

Step 2

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

$x = \pm \sqrt{- 25}$

Step 3

Simplify $\pm \sqrt{- 25}$ .

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Step 3.1

Rewrite $- 25$ as $- 1 (25)$ .

$x = \pm \sqrt{- 1 (25)}$

Step 3.2

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{25}$

Step 3.3

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

$x = \pm i \cdot \sqrt{25}$

Step 3.4

Rewrite $25$ as $5^{2}$ .

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

Step 3.5

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

$x = \pm i \cdot 5$

Step 3.6

Move $5$ to the left of $i$ .

$x = \pm 5 i$

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.

$x = 5 i$

Step 4.2

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

$x = - 5 i$

Step 4.3

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

$x = 5 i, - 5 i$