Finite Math Examples

$105000 {(1 + x)}^{12} = 170000$

Step 1

Divide each term in $105000 {(1 + x)}^{12} = 170000$ by $105000$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $105000 {(1 + x)}^{12} = 170000$ by $105000$ .

$\frac{105000 {(1 + x)}^{12}}{105000} = \frac{170000}{105000}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $105000$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{105000 {(1 + x)}^{12}}{105000} = \frac{170000}{105000}$

Step 1.2.1.2

Divide ${(1 + x)}^{12}$ by $1$ .

${(1 + x)}^{12} = \frac{170000}{105000}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Cancel the common factor of $170000$ and $105000$ .

Tap for more steps...

Step 1.3.1.1

Factor $5000$ out of $170000$ .

${(1 + x)}^{12} = \frac{5000 (34)}{105000}$

Step 1.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.3.1.2.1

Factor $5000$ out of $105000$ .

${(1 + x)}^{12} = \frac{5000 \cdot 34}{5000 \cdot 21}$

Step 1.3.1.2.2

Cancel the common factor.

${(1 + x)}^{12} = \frac{5000 \cdot 34}{5000 \cdot 21}$

Step 1.3.1.2.3

Rewrite the expression.

${(1 + x)}^{12} = \frac{34}{21}$

Step 2

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

$1 + x = \pm \sqrt[12]{\frac{34}{21}}$

Step 3

Rewrite $\sqrt[12]{\frac{34}{21}}$ as $\frac{\sqrt[12]{34}}{\sqrt[12]{21}}$ .

$1 + x = \pm \frac{\sqrt[12]{34}}{\sqrt[12]{21}}$

Step 4

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

Tap for more steps...

Step 4.1

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

$1 + x = \frac{\sqrt[12]{34}}{\sqrt[12]{21}}$

Step 4.2

Subtract $1$ from both sides of the equation.

$x = \frac{\sqrt[12]{34}}{\sqrt[12]{21}} - 1$

Step 4.3

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

$1 + x = - \frac{\sqrt[12]{34}}{\sqrt[12]{21}}$

Step 4.4

Subtract $1$ from both sides of the equation.

$x = - \frac{\sqrt[12]{34}}{\sqrt[12]{21}} - 1$

Step 4.5

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

$x = \frac{\sqrt[12]{34}}{\sqrt[12]{21}} - 1, - \frac{\sqrt[12]{34}}{\sqrt[12]{21}} - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt[12]{34}}{\sqrt[12]{21}} - 1, - \frac{\sqrt[12]{34}}{\sqrt[12]{21}} - 1$

Decimal Form:

$x = 0.04097021 \dots, - 2.04097021 \dots$