Finite Math Examples

$1900 = 1400 {(1 + \frac{r}{4})}^{36}$

Step 1

Rewrite the equation as $1400 {(1 + \frac{r}{4})}^{36} = 1900$ .

$1400 {(1 + \frac{r}{4})}^{36} = 1900$

Step 2

Divide each term in $1400 {(1 + \frac{r}{4})}^{36} = 1900$ by $1400$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $1400 {(1 + \frac{r}{4})}^{36} = 1900$ by $1400$ .

$\frac{1400 {(1 + \frac{r}{4})}^{36}}{1400} = \frac{1900}{1400}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $1400$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{1400 {(1 + \frac{r}{4})}^{36}}{1400} = \frac{1900}{1400}$

Step 2.2.1.2

Divide ${(1 + \frac{r}{4})}^{36}$ by $1$ .

${(1 + \frac{r}{4})}^{36} = \frac{1900}{1400}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Cancel the common factor of $1900$ and $1400$ .

Tap for more steps...

Step 2.3.1.1

Factor $100$ out of $1900$ .

${(1 + \frac{r}{4})}^{36} = \frac{100 (19)}{1400}$

Step 2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 2.3.1.2.1

Factor $100$ out of $1400$ .

${(1 + \frac{r}{4})}^{36} = \frac{100 \cdot 19}{100 \cdot 14}$

Step 2.3.1.2.2

Cancel the common factor.

${(1 + \frac{r}{4})}^{36} = \frac{100 \cdot 19}{100 \cdot 14}$

Step 2.3.1.2.3

Rewrite the expression.

${(1 + \frac{r}{4})}^{36} = \frac{19}{14}$

Step 3

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

$1 + \frac{r}{4} = \pm \sqrt[36]{\frac{19}{14}}$

Step 4

Rewrite $\sqrt[36]{\frac{19}{14}}$ as $\frac{\sqrt[36]{19}}{\sqrt[36]{14}}$ .

$1 + \frac{r}{4} = \pm \frac{\sqrt[36]{19}}{\sqrt[36]{14}}$

Step 5

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

Tap for more steps...

Step 5.1

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

$1 + \frac{r}{4} = \frac{\sqrt[36]{19}}{\sqrt[36]{14}}$

Step 5.2

Subtract $1$ from both sides of the equation.

$\frac{r}{4} = \frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1$

Step 5.3

Multiply both sides of the equation by $4$ .

$4 \frac{r}{4} = 4 (\frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$

Step 5.4

Simplify both sides of the equation.

Tap for more steps...

Step 5.4.1

Simplify the left side.

Tap for more steps...

Step 5.4.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.4.1.1.1

Cancel the common factor.

$4 \frac{r}{4} = 4 (\frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$

Step 5.4.1.1.2

Rewrite the expression.

$r = 4 (\frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$

Step 5.4.2

Simplify the right side.

Tap for more steps...

Step 5.4.2.1

Simplify $4 (\frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$ .

Tap for more steps...

Step 5.4.2.1.1

Apply the distributive property.

$r = 4 \frac{\sqrt[36]{19}}{\sqrt[36]{14}} + 4 \cdot - 1$

Step 5.4.2.1.2

Combine $4$ and $\frac{\sqrt[36]{19}}{\sqrt[36]{14}}$ .

$r = \frac{4 \sqrt[36]{19}}{\sqrt[36]{14}} + 4 \cdot - 1$

Step 5.4.2.1.3

Multiply $4$ by $- 1$ .

$r = \frac{4 \sqrt[36]{19}}{\sqrt[36]{14}} - 4$

Step 5.5

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

$1 + \frac{r}{4} = - \frac{\sqrt[36]{19}}{\sqrt[36]{14}}$

Step 5.6

Subtract $1$ from both sides of the equation.

$\frac{r}{4} = - \frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1$

Step 5.7

Multiply both sides of the equation by $4$ .

$4 \frac{r}{4} = 4 (- \frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$

Step 5.8

Simplify both sides of the equation.

Tap for more steps...

Step 5.8.1

Simplify the left side.

Tap for more steps...

Step 5.8.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 5.8.1.1.1

Cancel the common factor.

$4 \frac{r}{4} = 4 (- \frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$

Step 5.8.1.1.2

Rewrite the expression.

$r = 4 (- \frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$

Step 5.8.2

Simplify the right side.

Tap for more steps...

Step 5.8.2.1

Simplify $4 (- \frac{\sqrt[36]{19}}{\sqrt[36]{14}} - 1)$ .

Tap for more steps...

Step 5.8.2.1.1

Apply the distributive property.

$r = 4 (- \frac{\sqrt[36]{19}}{\sqrt[36]{14}}) + 4 \cdot - 1$

Step 5.8.2.1.2

Multiply $4 (- \frac{\sqrt[36]{19}}{\sqrt[36]{14}})$ .

Tap for more steps...

Step 5.8.2.1.2.1

Multiply $- 1$ by $4$ .

$r = - 4 \frac{\sqrt[36]{19}}{\sqrt[36]{14}} + 4 \cdot - 1$

Step 5.8.2.1.2.2

Combine $- 4$ and $\frac{\sqrt[36]{19}}{\sqrt[36]{14}}$ .

$r = \frac{- 4 \sqrt[36]{19}}{\sqrt[36]{14}} + 4 \cdot - 1$

Step 5.8.2.1.3

Multiply $4$ by $- 1$ .

$r = \frac{- 4 \sqrt[36]{19}}{\sqrt[36]{14}} - 4$

Step 5.8.2.1.4

Move the negative in front of the fraction.

$r = - \frac{4 \sqrt[36]{19}}{\sqrt[36]{14}} - 4$

Step 5.9

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

$r = \frac{4 \sqrt[36]{19}}{\sqrt[36]{14}} - 4, - \frac{4 \sqrt[36]{19}}{\sqrt[36]{14}} - 4$

Step 6

The result can be shown in multiple forms.

Exact Form:

$r = \frac{4 \sqrt[36]{19}}{\sqrt[36]{14}} - 4, - \frac{4 \sqrt[36]{19}}{\sqrt[36]{14}} - 4$

Decimal Form:

$r = 0.03407561 \dots, - 8.03407561 \dots$