Basic Math Examples

$7250 = 5100 {(1 + R)}^{120}$

Step 1

Rewrite the equation as $5100 {(1 + R)}^{120} = 7250$ .

$5100 {(1 + R)}^{120} = 7250$

Step 2

Divide each term in $5100 {(1 + R)}^{120} = 7250$ by $5100$ and simplify.

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Step 2.1

Divide each term in $5100 {(1 + R)}^{120} = 7250$ by $5100$ .

$\frac{5100 {(1 + R)}^{120}}{5100} = \frac{7250}{5100}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5100$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5100 {(1 + R)}^{120}}{5100} = \frac{7250}{5100}$

Step 2.2.1.2

Divide ${(1 + R)}^{120}$ by $1$ .

${(1 + R)}^{120} = \frac{7250}{5100}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $7250$ and $5100$ .

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Step 2.3.1.1

Factor $50$ out of $7250$ .

${(1 + R)}^{120} = \frac{50 (145)}{5100}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $50$ out of $5100$ .

${(1 + R)}^{120} = \frac{50 \cdot 145}{50 \cdot 102}$

Step 2.3.1.2.2

Cancel the common factor.

${(1 + R)}^{120} = \frac{50 \cdot 145}{50 \cdot 102}$

Step 2.3.1.2.3

Rewrite the expression.

${(1 + R)}^{120} = \frac{145}{102}$

Step 3

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

$1 + R = \pm \sqrt[120]{\frac{145}{102}}$

Step 4

Rewrite $\sqrt[120]{\frac{145}{102}}$ as $\frac{\sqrt[120]{145}}{\sqrt[120]{102}}$ .

$1 + R = \pm \frac{\sqrt[120]{145}}{\sqrt[120]{102}}$

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.

$1 + R = \frac{\sqrt[120]{145}}{\sqrt[120]{102}}$

Step 5.2

Subtract $1$ from both sides of the equation.

$R = \frac{\sqrt[120]{145}}{\sqrt[120]{102}} - 1$

Step 5.3

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

$1 + R = - \frac{\sqrt[120]{145}}{\sqrt[120]{102}}$

Step 5.4

Subtract $1$ from both sides of the equation.

$R = - \frac{\sqrt[120]{145}}{\sqrt[120]{102}} - 1$

Step 5.5

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

$R = \frac{\sqrt[120]{145}}{\sqrt[120]{102}} - 1, - \frac{\sqrt[120]{145}}{\sqrt[120]{102}} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$R = \frac{\sqrt[120]{145}}{\sqrt[120]{102}} - 1, - \frac{\sqrt[120]{145}}{\sqrt[120]{102}} - 1$

Decimal Form:

$R = 0.00293564 \dots, - 2.00293564 \dots$