Basic Math Examples

$80 = c^{2}$

Step 1

Rewrite the equation as $c^{2} = 80$ .

$c^{2} = 80$

Step 2

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

$c = \pm \sqrt{80}$

Step 3

Simplify $\pm \sqrt{80}$ .

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Step 3.1

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 3.1.1

Factor $16$ out of $80$ .

$c = \pm \sqrt{16 (5)}$

Step 3.1.2

Rewrite $16$ as $4^{2}$ .

$c = \pm \sqrt{4^{2} \cdot 5}$

Step 3.2

Pull terms out from under the radical.

$c = \pm 4 \sqrt{5}$

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.

$c = 4 \sqrt{5}$

Step 4.2

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

$c = - 4 \sqrt{5}$

Step 4.3

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

$c = 4 \sqrt{5}, - 4 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$c = 4 \sqrt{5}, - 4 \sqrt{5}$

Decimal Form:

$c = 8.94427190 \dots, - 8.94427190 \dots$