Finite Math Examples

$25 = \frac{1}{2} q^{2} + 30$

Step 1

Rewrite the equation as $\frac{1}{2} q^{2} + 30 = 25$ .

$\frac{1}{2} q^{2} + 30 = 25$

Step 2

Combine $\frac{1}{2}$ and $q^{2}$ .

$\frac{q^{2}}{2} + 30 = 25$

Step 3

Move all terms not containing $q$ to the right side of the equation.

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Step 3.1

Subtract $30$ from both sides of the equation.

$\frac{q^{2}}{2} = 25 - 30$

Step 3.2

Subtract $30$ from $25$ .

$\frac{q^{2}}{2} = - 5$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{q^{2}}{2} = 2 \cdot - 5$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1

Cancel the common factor.

$2 \frac{q^{2}}{2} = 2 \cdot - 5$

Step 5.1.1.2

Rewrite the expression.

$q^{2} = 2 \cdot - 5$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $2$ by $- 5$ .

$q^{2} = - 10$

Step 6

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

$q = \pm \sqrt{- 10}$

Step 7

Simplify $\pm \sqrt{- 10}$ .

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Step 7.1

Rewrite $- 10$ as $- 1 (10)$ .

$q = \pm \sqrt{- 1 (10)}$

Step 7.2

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$q = \pm \sqrt{- 1} \cdot \sqrt{10}$

Step 7.3

Rewrite $\sqrt{- 1}$ as $i$ .

$q = \pm i \sqrt{10}$

Step 8

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

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Step 8.1

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

$q = i \sqrt{10}$

Step 8.2

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

$q = - i \sqrt{10}$

Step 8.3

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

$q = i \sqrt{10}, - i \sqrt{10}$