Finite Math Examples

$1.065 = {(1 + \frac{x}{4})}^{4}$

Step 1

Rewrite the equation as ${(1 + \frac{x}{4})}^{4} = 1.065$ .

${(1 + \frac{x}{4})}^{4} = 1.065$

Step 2

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

$1 + \frac{x}{4} = \pm \sqrt[4]{1.065}$

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.

$1 + \frac{x}{4} = \sqrt[4]{1.065}$

Step 3.2

Subtract $1$ from both sides of the equation.

$\frac{x}{4} = \sqrt[4]{1.065} - 1$

Step 3.3

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (\sqrt[4]{1.065} - 1)$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Cancel the common factor of $4$ .

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Step 3.4.1.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 (\sqrt[4]{1.065} - 1)$

Step 3.4.1.1.2

Rewrite the expression.

$x = 4 (\sqrt[4]{1.065} - 1)$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $4 (\sqrt[4]{1.065} - 1)$ .

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Step 3.4.2.1.1

Apply the distributive property.

$x = 4 \sqrt[4]{1.065} + 4 \cdot - 1$

Step 3.4.2.1.2

Multiply $4$ by $- 1$ .

$x = 4 \sqrt[4]{1.065} - 4$

Step 3.5

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

$1 + \frac{x}{4} = - \sqrt[4]{1.065}$

Step 3.6

Subtract $1$ from both sides of the equation.

$\frac{x}{4} = - \sqrt[4]{1.065} - 1$

Step 3.7

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (- \sqrt[4]{1.065} - 1)$

Step 3.8

Simplify both sides of the equation.

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Step 3.8.1

Simplify the left side.

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Step 3.8.1.1

Cancel the common factor of $4$ .

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Step 3.8.1.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 (- \sqrt[4]{1.065} - 1)$

Step 3.8.1.1.2

Rewrite the expression.

$x = 4 (- \sqrt[4]{1.065} - 1)$

Step 3.8.2

Simplify the right side.

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Step 3.8.2.1

Simplify $4 (- \sqrt[4]{1.065} - 1)$ .

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Step 3.8.2.1.1

Apply the distributive property.

$x = 4 (- \sqrt[4]{1.065}) + 4 \cdot - 1$

Step 3.8.2.1.2

Multiply.

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Step 3.8.2.1.2.1

Multiply $- 1$ by $4$ .

$x = - 4 \sqrt[4]{1.065} + 4 \cdot - 1$

Step 3.8.2.1.2.2

Multiply $4$ by $- 1$ .

$x = - 4 \sqrt[4]{1.065} - 4$

Step 3.9

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

$x = 4 \sqrt[4]{1.065} - 4, - 4 \sqrt[4]{1.065} - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 4 \sqrt[4]{1.065} - 4, - 4 \sqrt[4]{1.065} - 4$

Decimal Form:

$x = 0.06347313 \dots, - 8.06347313 \dots$