Basic Math Examples

${(z - 8)}^{2} = - 5$

Step 1

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

$z - 8 = \pm \sqrt{- 5}$

Step 2

Simplify $\pm \sqrt{- 5}$ .

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Step 2.1

Rewrite $- 5$ as $- 1 (5)$ .

$z - 8 = \pm \sqrt{- 1 (5)}$

Step 2.2

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$z - 8 = \pm \sqrt{- 1} \cdot \sqrt{5}$

Step 2.3

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

$z - 8 = \pm i \sqrt{5}$

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.

$z - 8 = i \sqrt{5}$

Step 3.2

Add $8$ to both sides of the equation.

$z = i \sqrt{5} + 8$

Step 3.3

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

$z - 8 = - i \sqrt{5}$

Step 3.4

Add $8$ to both sides of the equation.

$z = - i \sqrt{5} + 8$

Step 3.5

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

$z = i \sqrt{5} + 8, - i \sqrt{5} + 8$