Finite Math Examples

$x^{5} = \frac{y^{2}}{33}$

Step 1

Rewrite the equation as $\frac{y^{2}}{33} = x^{5}$ .

$\frac{y^{2}}{33} = x^{5}$

Step 2

Multiply both sides of the equation by $33$ .

$33 \frac{y^{2}}{33} = 33 x^{5}$

Step 3

Simplify the left side.

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Step 3.1

Cancel the common factor of $33$ .

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Step 3.1.1

Cancel the common factor.

$33 \frac{y^{2}}{33} = 33 x^{5}$

Step 3.1.2

Rewrite the expression.

$y^{2} = 33 x^{5}$

Step 4

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

$y = \pm \sqrt{33 x^{5}}$

Step 5

Simplify $\pm \sqrt{33 x^{5}}$ .

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Step 5.1

Rewrite $33 x^{5}$ as ${(x^{2})}^{2} \cdot (33 x)$ .

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Step 5.1.1

Factor out $x^{4}$ .

$y = \pm \sqrt{33 (x^{4} x)}$

Step 5.1.2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$y = \pm \sqrt{33 ({(x^{2})}^{2} x)}$

Step 5.1.3

Reorder $33$ and ${(x^{2})}^{2}$ .

$y = \pm \sqrt{{(x^{2})}^{2} \cdot 33 x}$

Step 5.1.4

Add parentheses.

$y = \pm \sqrt{{(x^{2})}^{2} \cdot (33 x)}$

Step 5.2

Pull terms out from under the radical.

$y = \pm x^{2} \sqrt{33 x}$

Step 6

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

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Step 6.1

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

$y = x^{2} \sqrt{33 x}$

Step 6.2

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

$y = - x^{2} \sqrt{33 x}$

Step 6.3

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

$y = x^{2} \sqrt{33 x}$

$y = - x^{2} \sqrt{33 x}$

$y = x^{2} \sqrt{33 x}$

$y = - x^{2} \sqrt{33 x}$

Step 7

Set the radicand in $\sqrt{33 x}$ greater than or equal to $0$ to find where the expression is defined.

$33 x \geq 0$

Step 8

Divide each term in $33 x \geq 0$ by $33$ and simplify.

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Step 8.1

Divide each term in $33 x \geq 0$ by $33$ .

$\frac{33 x}{33} \geq \frac{0}{33}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $33$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{33 x}{33} \geq \frac{0}{33}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{0}{33}$

Step 8.3

Simplify the right side.

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Step 8.3.1

Divide $0$ by $33$ .

$x \geq 0$

Step 9

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 10