Basic Math Examples

$q = 54 p^{2} - 5 q$

Step 1

Rewrite the equation as $54 p^{2} - 5 q = q$ .

$54 p^{2} - 5 q = q$

Step 2

Move all terms not containing $p$ to the right side of the equation.

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Step 2.1

Add $5 q$ to both sides of the equation.

$54 p^{2} = q + 5 q$

Step 2.2

Add $q$ and $5 q$ .

$54 p^{2} = 6 q$

Step 3

Divide each term in $54 p^{2} = 6 q$ by $54$ and simplify.

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Step 3.1

Divide each term in $54 p^{2} = 6 q$ by $54$ .

$\frac{54 p^{2}}{54} = \frac{6 q}{54}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $54$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{54 p^{2}}{54} = \frac{6 q}{54}$

Step 3.2.1.2

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

$p^{2} = \frac{6 q}{54}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $6$ and $54$ .

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Step 3.3.1.1

Factor $6$ out of $6 q$ .

$p^{2} = \frac{6 (q)}{54}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $6$ out of $54$ .

$p^{2} = \frac{6 q}{6 \cdot 9}$

Step 3.3.1.2.2

Cancel the common factor.

$p^{2} = \frac{6 q}{6 \cdot 9}$

Step 3.3.1.2.3

Rewrite the expression.

$p^{2} = \frac{q}{9}$

Step 4

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

$p = \pm \sqrt{\frac{q}{9}}$

Step 5

Simplify $\pm \sqrt{\frac{q}{9}}$ .

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Step 5.1

Rewrite $\frac{q}{9}$ as ${(\frac{1}{3})}^{2} q$ .

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Step 5.1.1

Factor the perfect power $1^{2}$ out of $q$ .

$p = \pm \sqrt{\frac{1^{2} q}{9}}$

Step 5.1.2

Factor the perfect power $3^{2}$ out of $9$ .

$p = \pm \sqrt{\frac{1^{2} q}{3^{2} \cdot 1}}$

Step 5.1.3

Rearrange the fraction $\frac{1^{2} q}{3^{2} \cdot 1}$ .

$p = \pm \sqrt{{(\frac{1}{3})}^{2} q}$

Step 5.2

Pull terms out from under the radical.

$p = \pm \frac{1}{3} \sqrt{q}$

Step 5.3

Combine $\frac{1}{3}$ and $\sqrt{q}$ .

$p = \pm \frac{\sqrt{q}}{3}$

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.

$p = \frac{\sqrt{q}}{3}$

Step 6.2

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

$p = - \frac{\sqrt{q}}{3}$

Step 6.3

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

$p = \frac{\sqrt{q}}{3}$

$p = - \frac{\sqrt{q}}{3}$

$p = \frac{\sqrt{q}}{3}$

$p = - \frac{\sqrt{q}}{3}$