Basic Math Examples

$z^{2} = (2 \cdot 2 - 3 - (5 \cdot 2 - 2))$

Step 1

Multiply $2$ by $2$ .

$z^{2} = 4 - 3 - (5 \cdot 2 - 2)$

Step 2

Multiply $5$ by $2$ .

$z^{2} = 4 - 3 - (10 - 2)$

Step 3

Subtract $2$ from $10$ .

$z^{2} = 4 - 3 - 1 \cdot 8$

Step 4

Multiply $- 1$ by $8$ .

$z^{2} = 4 - 3 - 8$

Step 5

Subtract $3$ from $4$ .

$z^{2} = 1 - 8$

Step 6

Subtract $8$ from $1$ .

$z^{2} = - 7$

Step 7

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

$z = \pm \sqrt{- 7}$

Step 8

Simplify $\pm \sqrt{- 7}$ .

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Step 8.1

Rewrite $- 7$ as $- 1 (7)$ .

$z = \pm \sqrt{- 1 (7)}$

Step 8.2

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$z = \pm \sqrt{- 1} \cdot \sqrt{7}$

Step 8.3

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

$z = \pm i \sqrt{7}$

Step 9

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

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Step 9.1

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

$z = i \sqrt{7}$

Step 9.2

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

$z = - i \sqrt{7}$

Step 9.3

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

$z = i \sqrt{7}, - i \sqrt{7}$