Finite Math Examples

$181 (\frac{1 + {(\frac{x}{12})}^{360} - 1}{\frac{x}{12}}) = 192897$

Step 1

Simplify $181 (\frac{1 + {(\frac{x}{12})}^{360} - 1}{\frac{x}{12}})$ .

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Apply the product rule to $\frac{x}{12}$ .

$181 \frac{1 + \frac{x^{360}}{12^{360}} - 1}{\frac{x}{12}} = 192897$

Step 1.1.2

Subtract $1$ from $1$ .

$181 \frac{0 + \frac{x^{360}}{12^{360}}}{\frac{x}{12}} = 192897$

Step 1.1.3

Add $0$ and $\frac{x^{360}}{12^{360}}$ .

$181 \frac{\frac{x^{360}}{12^{360}}}{\frac{x}{12}} = 192897$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$181 (\frac{x^{360}}{12^{360}} \cdot \frac{12}{x}) = 192897$

Step 1.3

Combine.

$181 \frac{x^{360} \cdot 12}{12^{360} x} = 192897$

Step 1.4

Cancel the common factor of $x^{360}$ and $x$ .

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Step 1.4.1

Factor $x$ out of $x^{360} \cdot 12$ .

$181 \frac{x (x^{359} \cdot 12)}{12^{360} x} = 192897$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $x$ out of $12^{360} x$ .

$181 \frac{x (x^{359} \cdot 12)}{x \cdot 12^{360}} = 192897$

Step 1.4.2.2

Cancel the common factor.

$181 \frac{x (x^{359} \cdot 12)}{x \cdot 12^{360}} = 192897$

Step 1.4.2.3

Rewrite the expression.

$181 \frac{x^{359} \cdot 12}{12^{360}} = 192897$

Step 1.5

Cancel the common factor of $12$ and $12^{360}$ .

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Step 1.5.1

Factor $12$ out of $x^{359} \cdot 12$ .

$181 \frac{12 \cdot x^{359}}{12^{360}} = 192897$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $12$ out of $12^{360}$ .

$181 \frac{12 \cdot x^{359}}{12 \cdot 12^{359}} = 192897$

Step 1.5.2.2

Cancel the common factor.

$181 \frac{12 \cdot x^{359}}{12 \cdot 12^{359}} = 192897$

Step 1.5.2.3

Rewrite the expression.

$181 \frac{x^{359}}{12^{359}} = 192897$

Step 1.6

Combine $181$ and $\frac{x^{359}}{12^{359}}$ .

$\frac{181 x^{359}}{12^{359}} = 192897$

Step 2

Multiply both sides of the equation by $\frac{12^{359}}{181}$ .

$\frac{12^{359}}{181} \cdot \frac{181 x^{359}}{12^{359}} = \frac{12^{359}}{181} \cdot 192897$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{12^{359}}{181} \cdot \frac{181 x^{359}}{12^{359}}$ .

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Step 3.1.1.1

Combine.

$\frac{12^{359} (181 x^{359})}{181 \cdot 12^{359}} = \frac{12^{359}}{181} \cdot 192897$

Step 3.1.1.2

Cancel the common factor of $12^{359}$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{12^{359} (181 x^{359})}{181 \cdot 12^{359}} = \frac{12^{359}}{181} \cdot 192897$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{181 x^{359}}{181} = \frac{12^{359}}{181} \cdot 192897$

Step 3.1.1.3

Cancel the common factor of $181$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{181 x^{359}}{181} = \frac{12^{359}}{181} \cdot 192897$

Step 3.1.1.3.2

Divide $x^{359}$ by $1$ .

$x^{359} = \frac{12^{359}}{181} \cdot 192897$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{12^{359}}{181} \cdot 192897$ .

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Step 3.2.1.1

Combine $\frac{12^{359}}{181}$ and $192897$ .

$x^{359} = \frac{12^{359} \cdot 192897}{181}$

Step 3.2.1.2

Move $192897$ to the left of $12^{359}$ .

$x^{359} = \frac{192897 \cdot 12^{359}}{181}$

Step 4

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

$x = \sqrt[359]{\frac{192897 \cdot 12^{359}}{181}}$

Step 5

Simplify $\sqrt[359]{\frac{192897 \cdot 12^{359}}{181}}$ .

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Step 5.1

Rewrite $\sqrt[359]{\frac{192897 \cdot 12^{359}}{181}}$ as $\frac{\sqrt[359]{192897 \cdot 12^{359}}}{\sqrt[359]{181}}$ .

$x = \frac{\sqrt[359]{192897 \cdot 12^{359}}}{\sqrt[359]{181}}$

Step 5.2

Simplify the numerator.

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Step 5.2.1

Reorder $192897$ and $12^{359}$ .

$x = \frac{\sqrt[359]{12^{359} \cdot 192897}}{\sqrt[359]{181}}$

Step 5.2.2

Pull terms out from under the radical.

$x = \frac{12 \sqrt[359]{192897}}{\sqrt[359]{181}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12 \sqrt[359]{192897}}{\sqrt[359]{181}}$

Decimal Form:

$x = 12.23530508 \dots$