Finite Math Examples

$4124.82 = 3000 {(1 + x)}^{32}$

Step 1

Rewrite the equation as $3000 {(1 + x)}^{32} = 4124.82$ .

$3000 {(1 + x)}^{32} = 4124.82$

Step 2

Divide each term in $3000 {(1 + x)}^{32} = 4124.82$ by $3000$ and simplify.

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Step 2.1

Divide each term in $3000 {(1 + x)}^{32} = 4124.82$ by $3000$ .

$\frac{3000 {(1 + x)}^{32}}{3000} = \frac{4124.82}{3000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3000 {(1 + x)}^{32}}{3000} = \frac{4124.82}{3000}$

Step 2.2.1.2

Divide ${(1 + x)}^{32}$ by $1$ .

${(1 + x)}^{32} = \frac{4124.82}{3000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $4124.82$ by $3000$ .

${(1 + x)}^{32} = 1.37494$

Step 3

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

$1 + x = \pm \sqrt[32]{1.37494}$

Step 4

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

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Step 4.1

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

$1 + x = \sqrt[32]{1.37494}$

Step 4.2

Subtract $1$ from both sides of the equation.

$x = \sqrt[32]{1.37494} - 1$

Step 4.3

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

$1 + x = - \sqrt[32]{1.37494}$

Step 4.4

Subtract $1$ from both sides of the equation.

$x = - \sqrt[32]{1.37494} - 1$

Step 4.5

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

$x = \sqrt[32]{1.37494} - 1, - \sqrt[32]{1.37494} - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[32]{1.37494} - 1, - \sqrt[32]{1.37494} - 1$

Decimal Form:

$x = 0.00999998 \dots, - 2.00999998 \dots$