Algebra Examples

a = \frac{π d^{2}}{4}

$a = \frac{π d^{2}}{4}$

Step 1

Rewrite the equation as

\frac{π d^{2}}{4} = a

$\frac{π d^{2}}{4} = a$ .

$\frac{π d^{2}}{4} = a$

Step 2

Multiply both sides of the equation by

$\frac{4}{π}$ .

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

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify

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

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Step 3.1.1.1

Combine.

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

Step 3.1.1.2

Cancel the common factor of

$4$ .

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Step 3.1.1.2.1

Cancel the common factor.

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

Step 3.1.1.2.2

Rewrite the expression.

$\frac{π d^{2}}{π} = \frac{4}{π} a$

Step 3.1.1.3

Cancel the common factor of

$π$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{π d^{2}}{π} = \frac{4}{π} a$

Step 3.1.1.3.2

Divide

$d^{2}$ by

$1$ .

$d^{2} = \frac{4}{π} a$

Step 3.2

Simplify the right side.

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Step 3.2.1

Combine

$\frac{4}{π}$ and

$a$ .

$d^{2} = \frac{4 a}{π}$

Step 4

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 5

Simplify

$\pm \sqrt{\frac{4 a}{π}}$ .

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Step 5.1

Rewrite

$\sqrt{\frac{4 a}{π}}$ as

$\frac{\sqrt{4 a}}{\sqrt{π}}$ .

$d = \pm \frac{\sqrt{4 a}}{\sqrt{π}}$

Step 5.2

Simplify the numerator.

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Step 5.2.1

Rewrite

$4$ as

$2^{2}$ .

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

Step 5.2.2

Pull terms out from under the radical.

$d = \pm \frac{2 \sqrt{a}}{\sqrt{π}}$

Step 5.3

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 5.4

Combine and simplify the denominator.

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Step 5.4.1

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 5.4.2

Raise

$\sqrt{π}$ to the power of

$1$ .

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

Step 5.4.3

Raise

$\sqrt{π}$ to the power of

$1$ .

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

Step 5.4.4

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 5.4.5

Add

$1$ and

$1$ .

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

Step 5.4.6

Rewrite

${\sqrt{π}}^{2}$ as

$π$ .

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Step 5.4.6.1

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 5.4.6.2

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 5.4.6.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 5.4.6.4

Cancel the common factor of

$2$ .

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Step 5.4.6.4.1

Cancel the common factor.

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

Step 5.4.6.4.2

Rewrite the expression.

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

Step 5.4.6.5

Simplify.

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

Step 5.5

Combine using the product rule for radicals.

$d = \pm \frac{2 \sqrt{π a}}{π}$

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.

$d = \frac{2 \sqrt{π a}}{π}$

Step 6.2

Next, use the negative value of the

$\pm$ to find the second solution.

$d = - \frac{2 \sqrt{π a}}{π}$

Step 6.3

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

$d = \frac{2 \sqrt{π a}}{π}$

$d = - \frac{2 \sqrt{π a}}{π}$

$d = \frac{2 \sqrt{π a}}{π}$

$d = - \frac{2 \sqrt{π a}}{π}$