Basic Math Examples

$0.3 = \frac{1}{2} \cdot 1 \cdot v^{2}$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot 1 \cdot v^{2} = 0.3$ .

$\frac{1}{2} \cdot 1 \cdot v^{2} = 0.3$

Step 2

Multiply $\frac{1}{2}$ by $1$ .

$\frac{1}{2} \cdot v^{2} = 0.3$

Step 3

Multiply each term in $\frac{1}{2} v^{2} = 0.3$ by $2$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{1}{2} v^{2} = 0.3$ by $2$ .

$\frac{1}{2} v^{2} \cdot 2 = 0.3 \cdot 2$

Step 3.2

Simplify the left side.

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Step 3.2.1

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

$\frac{v^{2}}{2} \cdot 2 = 0.3 \cdot 2$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{v^{2}}{2} \cdot 2 = 0.3 \cdot 2$

Step 3.2.2.2

Rewrite the expression.

$v^{2} = 0.3 \cdot 2$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $0.3$ by $2$ .

$v^{2} = 0.6$

Step 4

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

$v = \pm \sqrt{0.6}$

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.

$v = \sqrt{0.6}$

Step 5.2

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

$v = - \sqrt{0.6}$

Step 5.3

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

$v = \sqrt{0.6}, - \sqrt{0.6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$v = \sqrt{0.6}, - \sqrt{0.6}$

Decimal Form:

$v = 0.77459666 \dots, - 0.77459666 \dots$