Calculus Examples

$- 2 x r^{- 2} + 4 p r = 0$

Step 1

Simplify each term.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 2 x \frac{1}{r^{2}} + 4 p r = 0$

Step 1.2

Multiply $- 2 x \frac{1}{r^{2}}$ .

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Step 1.2.1

Combine $- 2$ and $\frac{1}{r^{2}}$ .

$x \frac{- 2}{r^{2}} + 4 p r = 0$

Step 1.2.2

Combine $x$ and $\frac{- 2}{r^{2}}$ .

$\frac{x \cdot - 2}{r^{2}} + 4 p r = 0$

Step 1.3

Move $- 2$ to the left of $x$ .

$\frac{- 2 \cdot x}{r^{2}} + 4 p r = 0$

Step 1.4

Move the negative in front of the fraction.

$- \frac{2 x}{r^{2}} + 4 p r = 0$

Step 2

Subtract $4 p r$ from both sides of the equation.

$- \frac{2 x}{r^{2}} = - 4 p r$

Step 3

Divide each term in $- \frac{2 x}{r^{2}} = - 4 p r$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{2 x}{r^{2}} = - 4 p r$ by $- 1$ .

$\frac{- \frac{2 x}{r^{2}}}{- 1} = \frac{- 4 p r}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{2 x}{r^{2}}}{1} = \frac{- 4 p r}{- 1}$

Step 3.2.2

Divide $\frac{2 x}{r^{2}}$ by $1$ .

$\frac{2 x}{r^{2}} = \frac{- 4 p r}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative one from the denominator of $\frac{- 4 p r}{- 1}$ .

$\frac{2 x}{r^{2}} = - 1 \cdot (- 4 p r)$

Step 3.3.2

Rewrite $- 1 \cdot (- 4 p r)$ as $- (- 4 p r)$ .

$\frac{2 x}{r^{2}} = - (- 4 p r)$

Step 3.3.3

Multiply $- 4$ by $- 1$ .

$\frac{2 x}{r^{2}} = 4 p r$

Step 4

Multiply both sides by $r^{2}$ .

$\frac{2 x}{r^{2}} r^{2} = 4 p r \cdot r^{2}$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $r^{2}$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{2 x}{r^{2}} r^{2} = 4 p r \cdot r^{2}$

Step 5.1.1.2

Rewrite the expression.

$2 x = 4 p r \cdot r^{2}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $r$ by $r^{2}$ by adding the exponents.

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Step 5.2.1.1

Move $r^{2}$ .

$2 x = 4 p (r^{2} r)$

Step 5.2.1.2

Multiply $r^{2}$ by $r$ .

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Step 5.2.1.2.1

Raise $r$ to the power of $1$ .

$2 x = 4 p (r^{2} r^{1})$

Step 5.2.1.2.2

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

$2 x = 4 p r^{2 + 1}$

Step 5.2.1.3

Add $2$ and $1$ .

$2 x = 4 p r^{3}$

Step 6

Divide each term in $2 x = 4 p r^{3}$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 x = 4 p r^{3}$ by $2$ .

$\frac{2 x}{2} = \frac{4 p r^{3}}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{4 p r^{3}}{2}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{4 p r^{3}}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $4$ and $2$ .

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Step 6.3.1.1

Factor $2$ out of $4 p r^{3}$ .

$x = \frac{2 (2 p r^{3})}{2}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $2$ out of $2$ .

$x = \frac{2 (2 p r^{3})}{2 (1)}$

Step 6.3.1.2.2

Cancel the common factor.

$x = \frac{2 (2 p r^{3})}{2 \cdot 1}$

Step 6.3.1.2.3

Rewrite the expression.

$x = \frac{2 p r^{3}}{1}$

Step 6.3.1.2.4

Divide $2 p r^{3}$ by $1$ .

$x = 2 p r^{3}$