Finite Math Examples

$p = - 0.1 q^{2} - 0.2 + 9$

Step 1

Rewrite the equation as $- 0.1 q^{2} - 0.2 + 9 = p$ .

$- 0.1 q^{2} - 0.2 + 9 = p$

Step 2

Add $- 0.2$ and $9$ .

$- 0.1 q^{2} + 8.8 = p$

Step 3

Subtract $8.8$ from both sides of the equation.

$- 0.1 q^{2} = p - 8.8$

Step 4

Divide each term in $- 0.1 q^{2} = p - 8.8$ by $- 0.1$ and simplify.

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Step 4.1

Divide each term in $- 0.1 q^{2} = p - 8.8$ by $- 0.1$ .

$\frac{- 0.1 q^{2}}{- 0.1} = \frac{p}{- 0.1} + \frac{- 8.8}{- 0.1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 0.1$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 0.1 q^{2}}{- 0.1} = \frac{p}{- 0.1} + \frac{- 8.8}{- 0.1}$

Step 4.2.1.2

Divide $q^{2}$ by $1$ .

$q^{2} = \frac{p}{- 0.1} + \frac{- 8.8}{- 0.1}$

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

Move the negative in front of the fraction.

$q^{2} = - \frac{p}{0.1} + \frac{- 8.8}{- 0.1}$

Step 4.3.1.2

Multiply by $1$ .

$q^{2} = - \frac{1 p}{0.1} + \frac{- 8.8}{- 0.1}$

Step 4.3.1.3

Factor $0.1$ out of $0.1$ .

$q^{2} = - \frac{1 p}{0.1 (1)} + \frac{- 8.8}{- 0.1}$

Step 4.3.1.4

Separate fractions.

$q^{2} = - (\frac{1}{0.1} \cdot \frac{p}{1}) + \frac{- 8.8}{- 0.1}$

Step 4.3.1.5

Divide $1$ by $0.1$ .

$q^{2} = - (10 \frac{p}{1}) + \frac{- 8.8}{- 0.1}$

Step 4.3.1.6

Divide $p$ by $1$ .

$q^{2} = - (10 p) + \frac{- 8.8}{- 0.1}$

Step 4.3.1.7

Multiply $10$ by $- 1$ .

$q^{2} = - 10 p + \frac{- 8.8}{- 0.1}$

Step 4.3.1.8

Divide $- 8.8$ by $- 0.1$ .

$q^{2} = - 10 p + 88$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$q = \pm \sqrt{- 10 p + 88}$

Step 6

Factor $2$ out of $- 10 p + 88$ .

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Step 6.1

Factor $2$ out of $- 10 p$ .

$q = \pm \sqrt{2 (- 5 p) + 88}$

Step 6.2

Factor $2$ out of $88$ .

$q = \pm \sqrt{2 (- 5 p) + 2 (44)}$

Step 6.3

Factor $2$ out of $2 (- 5 p) + 2 (44)$ .

$q = \pm \sqrt{2 (- 5 p + 44)}$

Step 7

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

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Step 7.1

First, use the positive value of the $\pm$ to find the first solution.

$q = \sqrt{2 (- 5 p + 44)}$

Step 7.2

Next, use the negative value of the $\pm$ to find the second solution.

$q = - \sqrt{2 (- 5 p + 44)}$

Step 7.3

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

$q = \sqrt{2 (- 5 p + 44)}$

$q = - \sqrt{2 (- 5 p + 44)}$

$q = \sqrt{2 (- 5 p + 44)}$

$q = - \sqrt{2 (- 5 p + 44)}$