Basic Math Examples

$y = 0.5 z^{2} + 3$

Step 1

Rewrite the equation as $0.5 z^{2} + 3 = y$ .

$0.5 z^{2} + 3 = y$

Step 2

Subtract $3$ from both sides of the equation.

$0.5 z^{2} = y - 3$

Step 3

Divide each term in $0.5 z^{2} = y - 3$ by $0.5$ and simplify.

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Step 3.1

Divide each term in $0.5 z^{2} = y - 3$ by $0.5$ .

$\frac{0.5 z^{2}}{0.5} = \frac{y}{0.5} + \frac{- 3}{0.5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.5 z^{2}}{0.5} = \frac{y}{0.5} + \frac{- 3}{0.5}$

Step 3.2.1.2

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

$z^{2} = \frac{y}{0.5} + \frac{- 3}{0.5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply by $1$ .

$z^{2} = \frac{1 y}{0.5} + \frac{- 3}{0.5}$

Step 3.3.1.2

Factor $0.5$ out of $0.5$ .

$z^{2} = \frac{1 y}{0.5 (1)} + \frac{- 3}{0.5}$

Step 3.3.1.3

Separate fractions.

$z^{2} = \frac{1}{0.5} \cdot \frac{y}{1} + \frac{- 3}{0.5}$

Step 3.3.1.4

Divide $1$ by $0.5$ .

$z^{2} = 2 \frac{y}{1} + \frac{- 3}{0.5}$

Step 3.3.1.5

Divide $y$ by $1$ .

$z^{2} = 2 y + \frac{- 3}{0.5}$

Step 3.3.1.6

Divide $- 3$ by $0.5$ .

$z^{2} = 2 y - 6$

Step 4

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

$z = \pm \sqrt{2 y - 6}$

Step 5

Factor $2$ out of $2 y - 6$ .

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Step 5.1

Factor $2$ out of $2 y$ .

$z = \pm \sqrt{2 (y) - 6}$

Step 5.2

Factor $2$ out of $- 6$ .

$z = \pm \sqrt{2 y + 2 \cdot - 3}$

Step 5.3

Factor $2$ out of $2 y + 2 \cdot - 3$ .

$z = \pm \sqrt{2 (y - 3)}$

Step 6

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

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Step 6.1

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

$z = \sqrt{2 (y - 3)}$

Step 6.2

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

$z = - \sqrt{2 (y - 3)}$

Step 6.3

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

$z = \sqrt{2 (y - 3)}$

$z = - \sqrt{2 (y - 3)}$

$z = \sqrt{2 (y - 3)}$

$z = - \sqrt{2 (y - 3)}$