Solve for x S=2pi square root of x/p

$S = 2 π \sqrt{\frac{x}{p}}$

Rewrite the equation as $2 π \sqrt{\frac{x}{p}} = S$ .

$2 π \sqrt{\frac{x}{p}} = S$

To remove the radical on the left side of the equation, square both sides of the equation.

${(2 π \sqrt{\frac{x}{p}})}^{2} = S^{2}$

Simplify each side of the equation.

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

${(2 π {(\frac{x}{p})}^{\frac{1}{2}})}^{2} = S^{2}$

Simplify the left side.

Simplify ${(2 π {(\frac{x}{p})}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $\frac{x}{p}$ .

${(2 π \frac{x^{\frac{1}{2}}}{p^{\frac{1}{2}}})}^{2} = S^{2}$

Multiply $2 π \frac{x^{\frac{1}{2}}}{p^{\frac{1}{2}}}$ .

Combine $\frac{x^{\frac{1}{2}}}{p^{\frac{1}{2}}}$ and $2$ .

${(\frac{x^{\frac{1}{2}} \cdot 2}{p^{\frac{1}{2}}} π)}^{2} = S^{2}$

Combine $\frac{x^{\frac{1}{2}} \cdot 2}{p^{\frac{1}{2}}}$ and $π$ .

${(\frac{x^{\frac{1}{2}} \cdot 2 π}{p^{\frac{1}{2}}})}^{2} = S^{2}$

Move $2$ to the left of $x^{\frac{1}{2}}$ .

${(\frac{2 \cdot x^{\frac{1}{2}} π}{p^{\frac{1}{2}}})}^{2} = S^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 x^{\frac{1}{2}} π}{p^{\frac{1}{2}}}$ .

$\frac{{(2 x^{\frac{1}{2}} π)}^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Apply the product rule to $2 x^{\frac{1}{2}} π$ .

$\frac{{(2 x^{\frac{1}{2}})}^{2} π^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Apply the product rule to $2 x^{\frac{1}{2}}$ .

$\frac{2^{2} {(x^{\frac{1}{2}})}^{2} π^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Simplify the numerator.

Raise $2$ to the power of $2$ .

$\frac{4 {(x^{\frac{1}{2}})}^{2} π^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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

$\frac{4 x^{\frac{1}{2} \cdot 2} π^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 x^{\frac{1}{2} \cdot 2} π^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Rewrite the expression.

$\frac{4 x^{1} π^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Simplify.

$\frac{4 x π^{2}}{{(p^{\frac{1}{2}})}^{2}} = S^{2}$

Simplify the denominator.

Multiply the exponents in ${(p^{\frac{1}{2}})}^{2}$ .

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

$\frac{4 x π^{2}}{p^{\frac{1}{2} \cdot 2}} = S^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 x π^{2}}{p^{\frac{1}{2} \cdot 2}} = S^{2}$

Rewrite the expression.

$\frac{4 x π^{2}}{p^{1}} = S^{2}$

Simplify.

$\frac{4 x π^{2}}{p} = S^{2}$

Solve for $x$ .

Multiply both sides by $p$ .

$\frac{4 x π^{2}}{p} p = S^{2} p$

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

$\frac{4 x π^{2}}{p} p = S^{2} p$

Rewrite the expression.

$4 x π^{2} = S^{2} p$

Divide each term in $4 x π^{2} = S^{2} p$ by $4 π^{2}$ and simplify.

Divide each term in $4 x π^{2} = S^{2} p$ by $4 π^{2}$ .

$\frac{4 x π^{2}}{4 π^{2}} = \frac{S^{2} p}{4 π^{2}}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x π^{2}}{4 π^{2}} = \frac{S^{2} p}{4 π^{2}}$

Rewrite the expression.

$\frac{x π^{2}}{π^{2}} = \frac{S^{2} p}{4 π^{2}}$

Cancel the common factor of $π^{2}$ .

Cancel the common factor.

$\frac{x π^{2}}{π^{2}} = \frac{S^{2} p}{4 π^{2}}$

Divide $x$ by $1$ .

$x = \frac{S^{2} p}{4 π^{2}}$

Solve for x S=2pi square root of x/p

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