Algebra Examples

$K = \frac{1}{2} \cdot (m v^{2})$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (m v^{2}) = K$ .

$\frac{1}{2} \cdot (m v^{2}) = K$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (m v^{2})) = 2 K$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} \cdot (m v^{2}))$ .

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Step 3.1.1

Multiply $\frac{1}{2} (m v^{2})$ .

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Step 3.1.1.1

Combine $m$ and $\frac{1}{2}$ .

$2 (\frac{m}{2} v^{2}) = 2 K$

Step 3.1.1.2

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

$2 \frac{m v^{2}}{2} = 2 K$

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Cancel the common factor.

$2 \frac{m v^{2}}{2} = 2 K$

Step 3.1.2.2

Rewrite the expression.

$m v^{2} = 2 K$

Step 4

Divide each term in $m v^{2} = 2 K$ by $v^{2}$ and simplify.

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Step 4.1

Divide each term in $m v^{2} = 2 K$ by $v^{2}$ .

$\frac{m v^{2}}{v^{2}} = \frac{2 K}{v^{2}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor.

$\frac{m v^{2}}{v^{2}} = \frac{2 K}{v^{2}}$

Step 4.2.1.2

Divide $m$ by $1$ .

$m = \frac{2 K}{v^{2}}$