Finite Math Examples

$9 x^{2} \cdot (4 y^{2}) = 36$

Step 1

Multiply $4$ by $9$ .

$36 x^{2} \cdot y^{2} = 36$

Step 2

Divide each term in $36 x^{2} \cdot y^{2} = 36$ by $36 y^{2}$ and simplify.

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Step 2.1

Divide each term in $36 x^{2} \cdot y^{2} = 36$ by $36 y^{2}$ .

$\frac{36 x^{2} \cdot y^{2}}{36 y^{2}} = \frac{36}{36 y^{2}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $36$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{36 x^{2} \cdot y^{2}}{36 y^{2}} = \frac{36}{36 y^{2}}$

Step 2.2.1.2

Rewrite the expression.

$\frac{x^{2} \cdot y^{2}}{y^{2}} = \frac{36}{36 y^{2}}$

Step 2.2.2

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

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Step 2.2.2.1

Cancel the common factor.

$\frac{x^{2} \cdot y^{2}}{y^{2}} = \frac{36}{36 y^{2}}$

Step 2.2.2.2

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

$x^{2} = \frac{36}{36 y^{2}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $36$ .

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Step 2.3.1.1

Cancel the common factor.

$x^{2} = \frac{36}{36 y^{2}}$

Step 2.3.1.2

Rewrite the expression.

$x^{2} = \frac{1}{y^{2}}$

Step 3

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

$x = \pm \sqrt{\frac{1}{y^{2}}}$

Step 4

Simplify $\pm \sqrt{\frac{1}{y^{2}}}$ .

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Step 4.1

Rewrite $1$ as $1^{2}$ .

$x = \pm \sqrt{\frac{1^{2}}{y^{2}}}$

Step 4.2

Rewrite $\frac{1^{2}}{y^{2}}$ as ${(\frac{1}{y})}^{2}$ .

$x = \pm \sqrt{{(\frac{1}{y})}^{2}}$

Step 4.3

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{1}{y}$

Step 5

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

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Step 5.1

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

$x = \frac{1}{y}$

Step 5.2

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

$x = - \frac{1}{y}$

Step 5.3

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

$x = \frac{1}{y}$

$x = - \frac{1}{y}$

$x = \frac{1}{y}$

$x = - \frac{1}{y}$