Basic Math Examples

$y = - \frac{1}{2} z^{2}$

Step 1

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

$- \frac{1}{2} z^{2} = y$

Step 2

Multiply both sides of the equation by $- 2$ .

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

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

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

$- 2 (- \frac{z^{2}}{2}) = - 2 y$

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Move the leading negative in $- \frac{z^{2}}{2}$ into the numerator.

$- 2 \frac{- z^{2}}{2} = - 2 y$

Step 3.1.2.2

Factor $2$ out of $- 2$ .

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

Step 3.1.2.3

Cancel the common factor.

$2 \cdot - 1 \frac{- z^{2}}{2} = - 2 y$

Step 3.1.2.4

Rewrite the expression.

$- - z^{2} = - 2 y$

Step 3.1.3

Multiply.

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Step 3.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z^{2} = - 2 y$

Step 3.1.3.2

Multiply $z^{2}$ by $1$ .

$z^{2} = - 2 y$

Step 4

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

$z = \pm \sqrt{- 2 y}$

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.

$z = \sqrt{- 2 y}$

Step 5.2

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

$z = - \sqrt{- 2 y}$

Step 5.3

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

$z = \sqrt{- 2 y}$

$z = - \sqrt{- 2 y}$

$z = \sqrt{- 2 y}$

$z = - \sqrt{- 2 y}$