Basic Math Examples

$π q = - \frac{π}{2} + v ({(\frac{π}{2})}^{2} - q)$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$π q = - \frac{π}{2} + v (\frac{π^{2}}{2^{2}} - q)$

Step 1.1.2

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

$π q = - \frac{π}{2} + v (\frac{π^{2}}{4} - q)$

Step 1.2

Apply the distributive property.

$π q = - \frac{π}{2} + v \frac{π^{2}}{4} + v (- q)$

Step 1.3

Combine $v$ and $\frac{π^{2}}{4}$ .

$π q = - \frac{π}{2} + \frac{v π^{2}}{4} + v (- q)$

Step 1.4

Rewrite using the commutative property of multiplication.

$π q = - \frac{π}{2} + \frac{v π^{2}}{4} - v q$

Step 2

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

$π q + v q = - \frac{π}{2} + \frac{v π^{2}}{4}$

Step 3

Factor $q$ out of $π q + v q$ .

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Step 3.1

Factor $q$ out of $π q$ .

$q π + v q = - \frac{π}{2} + \frac{v π^{2}}{4}$

Step 3.2

Factor $q$ out of $v q$ .

$q π + q v = - \frac{π}{2} + \frac{v π^{2}}{4}$

Step 3.3

Factor $q$ out of $q π + q v$ .

$q (π + v) = - \frac{π}{2} + \frac{v π^{2}}{4}$

Step 4

Divide each term in $q (π + v) = - \frac{π}{2} + \frac{v π^{2}}{4}$ by $π + v$ and simplify.

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Step 4.1

Divide each term in $q (π + v) = - \frac{π}{2} + \frac{v π^{2}}{4}$ by $π + v$ .

$\frac{q (π + v)}{π + v} = \frac{- \frac{π}{2}}{π + v} + \frac{\frac{v π^{2}}{4}}{π + v}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $π + v$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{q (π + v)}{π + v} = \frac{- \frac{π}{2}}{π + v} + \frac{\frac{v π^{2}}{4}}{π + v}$

Step 4.2.1.2

Divide $q$ by $1$ .

$q = \frac{- \frac{π}{2}}{π + v} + \frac{\frac{v π^{2}}{4}}{π + v}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$q = \frac{- \frac{π}{2} + \frac{v π^{2}}{4}}{π + v}$

Step 4.3.2

Multiply the numerator and denominator of the fraction by $4$ .

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Step 4.3.2.1

Multiply $\frac{- \frac{π}{2} + \frac{v π^{2}}{4}}{π + v}$ by $\frac{4}{4}$ .

$q = \frac{4}{4} \cdot \frac{- \frac{π}{2} + \frac{v π^{2}}{4}}{π + v}$

Step 4.3.2.2

Combine.

$q = \frac{4 (- \frac{π}{2} + \frac{v π^{2}}{4})}{4 (π + v)}$

Step 4.3.3

Apply the distributive property.

$q = \frac{4 (- \frac{π}{2}) + 4 \frac{v π^{2}}{4}}{4 π + 4 v}$

Step 4.3.4

Simplify by cancelling.

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Step 4.3.4.1

Cancel the common factor of $2$ .

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Step 4.3.4.1.1

Move the leading negative in $- \frac{π}{2}$ into the numerator.

$q = \frac{4 \frac{- π}{2} + 4 \frac{v π^{2}}{4}}{4 π + 4 v}$

Step 4.3.4.1.2

Factor $2$ out of $4$ .

$q = \frac{2 (2) \frac{- π}{2} + 4 \frac{v π^{2}}{4}}{4 π + 4 v}$

Step 4.3.4.1.3

Cancel the common factor.

$q = \frac{2 \cdot 2 \frac{- π}{2} + 4 \frac{v π^{2}}{4}}{4 π + 4 v}$

Step 4.3.4.1.4

Rewrite the expression.

$q = \frac{2 (- π) + 4 \frac{v π^{2}}{4}}{4 π + 4 v}$

Step 4.3.4.2

Multiply $- 1$ by $2$ .

$q = \frac{- 2 π + 4 \frac{v π^{2}}{4}}{4 π + 4 v}$

Step 4.3.4.3

Cancel the common factor of $4$ .

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Step 4.3.4.3.1

Cancel the common factor.

$q = \frac{- 2 π + 4 \frac{v π^{2}}{4}}{4 π + 4 v}$

Step 4.3.4.3.2

Rewrite the expression.

$q = \frac{- 2 π + v π^{2}}{4 π + 4 v}$

Step 4.3.5

Simplify with factoring out.

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Step 4.3.5.1

Factor $4$ out of $4 π + 4 v$ .

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Step 4.3.5.1.1

Factor $4$ out of $4 π$ .

$q = \frac{- 2 π + v π^{2}}{4 (π) + 4 v}$

Step 4.3.5.1.2

Factor $4$ out of $4 v$ .

$q = \frac{- 2 π + v π^{2}}{4 (π) + 4 (v)}$

Step 4.3.5.1.3

Factor $4$ out of $4 (π) + 4 (v)$ .

$q = \frac{- 2 π + v π^{2}}{4 (π + v)}$

Step 4.3.5.2

Factor $- 1$ out of $- 2 π$ .

$q = \frac{- (2 π) + v π^{2}}{4 (π + v)}$

Step 4.3.5.3

Factor $- 1$ out of $v π^{2}$ .

$q = \frac{- (2 π) - (- v π^{2})}{4 (π + v)}$

Step 4.3.5.4

Factor $- 1$ out of $- (2 π) - (- v π^{2})$ .

$q = \frac{- (2 π - v π^{2})}{4 (π + v)}$

Step 4.3.5.5

Simplify the expression.

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Step 4.3.5.5.1

Rewrite $- (2 π - v π^{2})$ as $- 1 (2 π - v π^{2})$ .

$q = \frac{- 1 (2 π - v π^{2})}{4 (π + v)}$

Step 4.3.5.5.2

Move the negative in front of the fraction.

$q = - \frac{2 π - v π^{2}}{4 (π + v)}$