Finite Math Examples

$9^{2} + 3^{2} + c^{2} = 0$

Step 1

Simplify $9^{2} + 3^{2} + c^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Raise $9$ to the power of $2$ .

$81 + 3^{2} + c^{2} = 0$

Step 1.1.2

Raise $3$ to the power of $2$ .

$81 + 9 + c^{2} = 0$

Step 1.2

Add $81$ and $9$ .

$90 + c^{2} = 0$

Step 2

Subtract $90$ from both sides of the equation.

$c^{2} = - 90$

Step 3

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

$c = \pm \sqrt{- 90}$

Step 4

Simplify $\pm \sqrt{- 90}$ .

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Step 4.1

Rewrite $- 90$ as $- 1 (90)$ .

$c = \pm \sqrt{- 1 (90)}$

Step 4.2

Rewrite $\sqrt{- 1 (90)}$ as $\sqrt{- 1} \cdot \sqrt{90}$ .

$c = \pm \sqrt{- 1} \cdot \sqrt{90}$

Step 4.3

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

$c = \pm i \cdot \sqrt{90}$

Step 4.4

Rewrite $90$ as $3^{2} \cdot 10$ .

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Step 4.4.1

Factor $9$ out of $90$ .

$c = \pm i \cdot \sqrt{9 (10)}$

Step 4.4.2

Rewrite $9$ as $3^{2}$ .

$c = \pm i \cdot \sqrt{3^{2} \cdot 10}$

Step 4.5

Pull terms out from under the radical.

$c = \pm i \cdot (3 \sqrt{10})$

Step 4.6

Move $3$ to the left of $i$ .

$c = \pm 3 i \sqrt{10}$

Step 5

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

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Step 5.1

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

$c = 3 i \sqrt{10}$

Step 5.2

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

$c = - 3 i \sqrt{10}$

Step 5.3

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

$c = 3 i \sqrt{10}, - 3 i \sqrt{10}$