Finite Math Examples

$z = 4 - x^{2} - y^{2}$

Step 1

Rewrite the equation as $4 - x^{2} - y^{2} = z$ .

$4 - x^{2} - y^{2} = z$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $4$ from both sides of the equation.

$- x^{2} - y^{2} = z - 4$

Step 2.2

Add $y^{2}$ to both sides of the equation.

$- x^{2} = z - 4 + y^{2}$

Step 3

Divide each term in $- x^{2} = z - 4 + y^{2}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x^{2} = z - 4 + y^{2}$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{z}{- 1} + \frac{- 4}{- 1} + \frac{y^{2}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{z}{- 1} + \frac{- 4}{- 1} + \frac{y^{2}}{- 1}$

Step 3.2.2

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

$x^{2} = \frac{z}{- 1} + \frac{- 4}{- 1} + \frac{y^{2}}{- 1}$

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

Move the negative one from the denominator of $\frac{z}{- 1}$ .

$x^{2} = - 1 \cdot z + \frac{- 4}{- 1} + \frac{y^{2}}{- 1}$

Step 3.3.1.2

Rewrite $- 1 \cdot z$ as $- z$ .

$x^{2} = - z + \frac{- 4}{- 1} + \frac{y^{2}}{- 1}$

Step 3.3.1.3

Divide $- 4$ by $- 1$ .

$x^{2} = - z + 4 + \frac{y^{2}}{- 1}$

Step 3.3.1.4

Move the negative one from the denominator of $\frac{y^{2}}{- 1}$ .

$x^{2} = - z + 4 - 1 \cdot y^{2}$

Step 3.3.1.5

Rewrite $- 1 \cdot y^{2}$ as $- y^{2}$ .

$x^{2} = - z + 4 - y^{2}$

Step 4

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

$x = \pm \sqrt{- z + 4 - y^{2}}$

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.

$x = \sqrt{- z + 4 - y^{2}}$

Step 5.2

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

$x = - \sqrt{- z + 4 - y^{2}}$

Step 5.3

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

$x = \sqrt{- z + 4 - y^{2}}$

$x = - \sqrt{- z + 4 - y^{2}}$

$x = \sqrt{- z + 4 - y^{2}}$

$x = - \sqrt{- z + 4 - y^{2}}$