Solve for x y=1/2x^2

$y = \frac{1}{2} x^{2}$

Step 1

Rewrite the equation as $\frac{1}{2} x^{2} = y$ .

$\frac{1}{2} x^{2} = y$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} x^{2}) = 2 y$

Step 3

Simplify the left side.

Simplify $2 (\frac{1}{2} x^{2})$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{2} = 2 y$

Step 4

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

$x = \pm \sqrt{2 y}$

Step 5

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

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

$x = \sqrt{2 y}$

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

$x = - \sqrt{2 y}$

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

$x = \sqrt{2 y}$

$x = - \sqrt{2 y}$

$x = \sqrt{2 y}$

$x = - \sqrt{2 y}$