Pre-Algebra Examples

$2.5 = \frac{v^{2}}{1.2 \cdot 9.8}$

Step 1

Rewrite the equation as $\frac{v^{2}}{1.2 \cdot 9.8} = 2.5$ .

$\frac{v^{2}}{1.2 \cdot 9.8} = 2.5$

Step 2

Multiply both sides of the equation by $1.2 \cdot 9.8$ .

$1.2 \cdot 9.8 \frac{v^{2}}{1.2 \cdot 9.8} = 1.2 \cdot 9.8 \cdot 2.5$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $1.2 \cdot 9.8 \frac{v^{2}}{1.2 \cdot 9.8}$ .

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Step 3.1.1.1

Multiply.

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Step 3.1.1.1.1

Multiply $1.2$ by $9.8$ .

$11.76 \frac{v^{2}}{1.2 \cdot 9.8} = 1.2 \cdot 9.8 \cdot 2.5$

Step 3.1.1.1.2

Multiply $1.2$ by $9.8$ .

$11.76 \frac{v^{2}}{11.76} = 1.2 \cdot 9.8 \cdot 2.5$

Step 3.1.1.2

Cancel the common factor of $11.76$ .

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Step 3.1.1.2.1

Cancel the common factor.

$11.76 \frac{v^{2}}{11.76} = 1.2 \cdot 9.8 \cdot 2.5$

Step 3.1.1.2.2

Rewrite the expression.

$v^{2} = 1.2 \cdot 9.8 \cdot 2.5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $1.2 \cdot 9.8 \cdot 2.5$ .

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Step 3.2.1.1

Multiply $1.2$ by $9.8$ .

$v^{2} = 11.76 \cdot 2.5$

Step 3.2.1.2

Multiply $11.76$ by $2.5$ .

$v^{2} = 29.4$

Step 4

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

$v = \pm \sqrt{29.4}$

Step 5

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

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Step 5.1

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

$v = \sqrt{29.4}$

Step 5.2

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

$v = - \sqrt{29.4}$

Step 5.3

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

$v = \sqrt{29.4}, - \sqrt{29.4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$v = \sqrt{29.4}, - \sqrt{29.4}$

Decimal Form:

$v = 5.42217668 \dots, - 5.42217668 \dots$