Algebra Examples

$a = π \frac{d^{2}}{4}$

Step 1

Rewrite the equation as $π (\frac{d^{2}}{4}) = a$ .

$π (\frac{d^{2}}{4}) = a$

Step 2

Combine $π$ and $\frac{d^{2}}{4}$ .

$\frac{π d^{2}}{4} = a$

Step 3

Multiply both sides of the equation by $\frac{4}{π}$ .

$\frac{4}{π} \cdot \frac{π d^{2}}{4} = \frac{4}{π} a$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{4}{π} \cdot \frac{π d^{2}}{4}$ .

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Step 4.1.1.1

Combine.

$\frac{4 (π d^{2})}{π \cdot 4} = \frac{4}{π} a$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{4 (π d^{2})}{π \cdot 4} = \frac{4}{π} a$

Step 4.1.1.2.2

Rewrite the expression.

$\frac{π d^{2}}{π} = \frac{4}{π} a$

Step 4.1.1.3

Cancel the common factor of $π$ .

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Step 4.1.1.3.1

Cancel the common factor.

$\frac{π d^{2}}{π} = \frac{4}{π} a$

Step 4.1.1.3.2

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

$d^{2} = \frac{4}{π} a$

Step 4.2

Simplify the right side.

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Step 4.2.1

Combine $\frac{4}{π}$ and $a$ .

$d^{2} = \frac{4 a}{π}$

Step 5

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

$d = \pm \sqrt{\frac{4 a}{π}}$

Step 6

Simplify $\pm \sqrt{\frac{4 a}{π}}$ .

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Step 6.1

Rewrite $\sqrt{\frac{4 a}{π}}$ as $\frac{\sqrt{4 a}}{\sqrt{π}}$ .

$d = \pm \frac{\sqrt{4 a}}{\sqrt{π}}$

Step 6.2

Simplify the numerator.

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Step 6.2.1

Rewrite $4$ as $2^{2}$ .

$d = \pm \frac{\sqrt{2^{2} a}}{\sqrt{π}}$

Step 6.2.2

Pull terms out from under the radical.

$d = \pm \frac{2 \sqrt{a}}{\sqrt{π}}$

Step 6.3

Multiply $\frac{2 \sqrt{a}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

$d = \pm \frac{2 \sqrt{a}}{\sqrt{π}} \cdot \frac{\sqrt{π}}{\sqrt{π}}$

Step 6.4

Combine and simplify the denominator.

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Step 6.4.1

Multiply $\frac{2 \sqrt{a}}{\sqrt{π}}$ by $\frac{\sqrt{π}}{\sqrt{π}}$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{\sqrt{π} \sqrt{π}}$

Step 6.4.2

Raise $\sqrt{π}$ to the power of $1$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{1} \sqrt{π}}$

Step 6.4.3

Raise $\sqrt{π}$ to the power of $1$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{1} {\sqrt{π}}^{1}}$

Step 6.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{1 + 1}}$

Step 6.4.5

Add $1$ and $1$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{\sqrt{π}}^{2}}$

Step 6.4.6

Rewrite ${\sqrt{π}}^{2}$ as $π$ .

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Step 6.4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{π}$ as $π^{\frac{1}{2}}$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{{(π^{\frac{1}{2}})}^{2}}$

Step 6.4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{\frac{1}{2} \cdot 2}}$

Step 6.4.6.3

Combine $\frac{1}{2}$ and $2$ .

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{\frac{2}{2}}}$

Step 6.4.6.4

Cancel the common factor of $2$ .

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Step 6.4.6.4.1

Cancel the common factor.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{\frac{2}{2}}}$

Step 6.4.6.4.2

Rewrite the expression.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π^{1}}$

Step 6.4.6.5

Simplify.

$d = \pm \frac{2 \sqrt{a} \sqrt{π}}{π}$

Step 6.5

Combine using the product rule for radicals.

$d = \pm \frac{2 \sqrt{π a}}{π}$

Step 7

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

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Step 7.1

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

$d = \frac{2 \sqrt{π a}}{π}$

Step 7.2

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

$d = - \frac{2 \sqrt{π a}}{π}$

Step 7.3

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

$d = \frac{2 \sqrt{π a}}{π}$

$d = - \frac{2 \sqrt{π a}}{π}$

$d = \frac{2 \sqrt{π a}}{π}$

$d = - \frac{2 \sqrt{π a}}{π}$