Algebra Examples

$y = \frac{v^{2}}{2 a}$

Step 1

Rewrite the equation as $\frac{v^{2}}{2 a} = y$ .

$\frac{v^{2}}{2 a} = y$

Step 2

Multiply both sides by $2 a$ .

$\frac{v^{2}}{2 a} (2 a) = y (2 a)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{v^{2}}{2 a} (2 a)$ .

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Step 3.1.1.1

Rewrite using the commutative property of multiplication.

$2 \frac{v^{2}}{2 a} a = y (2 a)$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 a$ .

$2 \frac{v^{2}}{2 (a)} a = y (2 a)$

Step 3.1.1.2.2

Cancel the common factor.

$2 \frac{v^{2}}{2 a} a = y (2 a)$

Step 3.1.1.2.3

Rewrite the expression.

$\frac{v^{2}}{a} a = y (2 a)$

Step 3.1.1.3

Cancel the common factor of $a$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{v^{2}}{a} a = y (2 a)$

Step 3.1.1.3.2

Rewrite the expression.

$v^{2} = y (2 a)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$v^{2} = 2 y a$

Step 4

Solve for $v$ .

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Step 4.1

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

$v = \pm \sqrt{2 y a}$

Step 4.2

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

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Step 4.2.1

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

$v = \sqrt{2 y a}$

Step 4.2.2

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

$v = - \sqrt{2 y a}$

Step 4.2.3

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

$v = \sqrt{2 y a}$

$v = - \sqrt{2 y a}$

$v = \sqrt{2 y a}$

$v = - \sqrt{2 y a}$

$v = \sqrt{2 y a}$

$v = - \sqrt{2 y a}$