Finite Math Examples

$x (50) = 3900 {(\frac{1}{2})}^{\frac{50}{14}}$

Step 1

Subtract $3900 {(\frac{1}{2})}^{\frac{50}{14}}$ from both sides of the equation.

$x (50) - 3900 {(\frac{1}{2})}^{\frac{50}{14}} = 0$

Step 2

Simplify each term.

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Step 2.1

Move $50$ to the left of $x$ .

$50 x - 3900 {(\frac{1}{2})}^{\frac{50}{14}} = 0$

Step 2.2

Cancel the common factor of $50$ and $14$ .

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Step 2.2.1

Factor $2$ out of $50$ .

$50 x - 3900 {(\frac{1}{2})}^{\frac{2 (25)}{14}} = 0$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $14$ .

$50 x - 3900 {(\frac{1}{2})}^{\frac{2 \cdot 25}{2 \cdot 7}} = 0$

Step 2.2.2.2

Cancel the common factor.

$50 x - 3900 {(\frac{1}{2})}^{\frac{2 \cdot 25}{2 \cdot 7}} = 0$

Step 2.2.2.3

Rewrite the expression.

$50 x - 3900 {(\frac{1}{2})}^{\frac{25}{7}} = 0$

Step 2.3

Apply the product rule to $\frac{1}{2}$ .

$50 x - 3900 \frac{1^{\frac{25}{7}}}{2^{\frac{25}{7}}} = 0$

Step 2.4

One to any power is one.

$50 x - 3900 \frac{1}{2^{\frac{25}{7}}} = 0$

Step 2.5

Combine $- 3900$ and $\frac{1}{2^{\frac{25}{7}}}$ .

$50 x + \frac{- 3900}{2^{\frac{25}{7}}} = 0$

Step 2.6

Move the negative in front of the fraction.

$50 x - \frac{3900}{2^{\frac{25}{7}}} = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.