Finite Math Examples

$1.12 = (\frac{39.4784176}{g^{2}}) \cdot 30.5$

Step 1

Rewrite the equation as $\frac{39.4784176}{g^{2}} \cdot 30.5 = 1.12$ .

$\frac{39.4784176}{g^{2}} \cdot 30.5 = 1.12$

Step 2

Multiply $\frac{39.4784176}{g^{2}} \cdot 30.5$ .

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Step 2.1

Combine $\frac{39.4784176}{g^{2}}$ and $30.5$ .

$\frac{39.4784176 \cdot 30.5}{g^{2}} = 1.12$

Step 2.2

Multiply $39.4784176$ by $30.5$ .

$\frac{1204.0917368}{g^{2}} = 1.12$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$g^{2}, 1$

Step 3.2

The LCM of one and any expression is the expression.

$g^{2}$

Step 4

Multiply each term in $\frac{1204.0917368}{g^{2}} = 1.12$ by $g^{2}$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{1204.0917368}{g^{2}} = 1.12$ by $g^{2}$ .

$\frac{1204.0917368}{g^{2}} g^{2} = 1.12 g^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $g^{2}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{1204.0917368}{g^{2}} g^{2} = 1.12 g^{2}$

Step 4.2.1.2

Rewrite the expression.

$1204.0917368 = 1.12 g^{2}$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $1.12 g^{2} = 1204.0917368$ .

$1.12 g^{2} = 1204.0917368$

Step 5.2

Divide each term in $1.12 g^{2} = 1204.0917368$ by $1.12$ and simplify.

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Step 5.2.1

Divide each term in $1.12 g^{2} = 1204.0917368$ by $1.12$ .

$\frac{1.12 g^{2}}{1.12} = \frac{1204.0917368}{1.12}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $1.12$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{1.12 g^{2}}{1.12} = \frac{1204.0917368}{1.12}$

Step 5.2.2.1.2

Divide $g^{2}$ by $1$ .

$g^{2} = \frac{1204.0917368}{1.12}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $1204.0917368$ by $1.12$ .

$g^{2} = 1075.08190785$

Step 5.3

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

$g = \pm \sqrt{1075.08190785}$

Step 5.4

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

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Step 5.4.1

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

$g = \sqrt{1075.08190785}$

Step 5.4.2

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

$g = - \sqrt{1075.08190785}$

Step 5.4.3

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

$g = \sqrt{1075.08190785}, - \sqrt{1075.08190785}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$g = \sqrt{1075.08190785}, - \sqrt{1075.08190785}$

Decimal Form:

$g = 32.78844168 \dots, - 32.78844168 \dots$