Calculus Examples

$y = \frac{x^{2}}{3}$

Step 1

Rewrite the equation as $\frac{x^{2}}{3} = y$ .

$\frac{x^{2}}{3} = y$

Step 2

Multiply both sides of the equation by $3$ .

$3 \frac{x^{2}}{3} = 3 y$

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$3 \frac{x^{2}}{3} = 3 y$

Step 3.1.2

Rewrite the expression.

$x^{2} = 3 y$

Step 4

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

$x = \pm \sqrt{3 y}$

Step 5

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

Tap for more steps...

Step 5.1

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

$x = \sqrt{3 y}$

Step 5.2

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

$x = - \sqrt{3 y}$

Step 5.3

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

$x = \sqrt{3 y}$

$x = - \sqrt{3 y}$

$x = \sqrt{3 y}$

$x = - \sqrt{3 y}$