Pre-Algebra Examples

${(n - 9)}^{2} = - 4$

Step 1

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

$n - 9 = \pm \sqrt{- 4}$

Step 2

Simplify $\pm \sqrt{- 4}$ .

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Step 2.1

Rewrite $- 4$ as $- 1 (4)$ .

$n - 9 = \pm \sqrt{- 1 (4)}$

Step 2.2

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$n - 9 = \pm \sqrt{- 1} \cdot \sqrt{4}$

Step 2.3

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

$n - 9 = \pm i \cdot \sqrt{4}$

Step 2.4

Rewrite $4$ as $2^{2}$ .

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

Step 2.5

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

$n - 9 = \pm i \cdot 2$

Step 2.6

Move $2$ to the left of $i$ .

$n - 9 = \pm 2 i$

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.

$n - 9 = 2 i$

Step 3.2

Move all terms not containing $n$ to the right side of the equation.

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Step 3.2.1

Add $9$ to both sides of the equation.

$n = 2 i + 9$

Step 3.2.2

Reorder $2 i$ and $9$ .

$n = 9 + 2 i$

Step 3.3

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

$n - 9 = - 2 i$

Step 3.4

Move all terms not containing $n$ to the right side of the equation.

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Step 3.4.1

Add $9$ to both sides of the equation.

$n = - 2 i + 9$

Step 3.4.2

Reorder $- 2 i$ and $9$ .

$n = 9 - 2 i$

Step 3.5

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

$n = 9 + 2 i, 9 - 2 i$