Finite Math Examples

$p = D {(q)}^{2} \cdot 4 - 1.25 q$

Step 1

Rewrite the equation as $D q^{2} \cdot 4 - 1.25 q = p$ .

$D q^{2} \cdot 4 - 1.25 q = p$

Step 2

Move $4$ to the left of $D q^{2}$ .

$4 D q^{2} - 1.25 q = p$

Step 3

Add $1.25 q$ to both sides of the equation.

$4 D q^{2} = p + 1.25 q$

Step 4

Divide each term in $4 D q^{2} = p + 1.25 q$ by $4 q^{2}$ and simplify.

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Step 4.1

Divide each term in $4 D q^{2} = p + 1.25 q$ by $4 q^{2}$ .

$\frac{4 D q^{2}}{4 q^{2}} = \frac{p}{4 q^{2}} + \frac{1.25 q}{4 q^{2}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 D q^{2}}{4 q^{2}} = \frac{p}{4 q^{2}} + \frac{1.25 q}{4 q^{2}}$

Step 4.2.1.2

Rewrite the expression.

$\frac{D q^{2}}{q^{2}} = \frac{p}{4 q^{2}} + \frac{1.25 q}{4 q^{2}}$

Step 4.2.2

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

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Step 4.2.2.1

Cancel the common factor.

$\frac{D q^{2}}{q^{2}} = \frac{p}{4 q^{2}} + \frac{1.25 q}{4 q^{2}}$

Step 4.2.2.2

Divide $D$ by $1$ .

$D = \frac{p}{4 q^{2}} + \frac{1.25 q}{4 q^{2}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $q$ and $q^{2}$ .

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Step 4.3.1.1.1

Factor $q$ out of $1.25 q$ .

$D = \frac{p}{4 q^{2}} + \frac{q \cdot 1.25}{4 q^{2}}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Factor $q$ out of $4 q^{2}$ .

$D = \frac{p}{4 q^{2}} + \frac{q \cdot 1.25}{q (4 q)}$

Step 4.3.1.1.2.2

Cancel the common factor.

$D = \frac{p}{4 q^{2}} + \frac{q \cdot 1.25}{q (4 q)}$

Step 4.3.1.1.2.3

Rewrite the expression.

$D = \frac{p}{4 q^{2}} + \frac{1.25}{4 q}$

Step 4.3.1.2

Factor $1.25$ out of $1.25$ .

$D = \frac{p}{4 q^{2}} + \frac{1.25 (1)}{4 q}$

Step 4.3.1.3

Factor $4$ out of $4 q$ .

$D = \frac{p}{4 q^{2}} + \frac{1.25 (1)}{4 (q)}$

Step 4.3.1.4

Separate fractions.

$D = \frac{p}{4 q^{2}} + \frac{1.25}{4} \cdot \frac{1}{q}$

Step 4.3.1.5

Divide $1.25$ by $4$ .

$D = \frac{p}{4 q^{2}} + 0.3125 \frac{1}{q}$

Step 4.3.1.6

Combine $0.3125$ and $\frac{1}{q}$ .

$D = \frac{p}{4 q^{2}} + \frac{0.3125}{q}$