Finite Math Examples

$x^{2} + {(y - 2)}^{2} = 36$

Step 1

Subtract ${(y - 2)}^{2}$ from both sides of the equation.

$x^{2} = 36 - {(y - 2)}^{2}$

Step 2

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

$x = \pm \sqrt{36 - {(y - 2)}^{2}}$

Step 3

Simplify $\pm \sqrt{36 - {(y - 2)}^{2}}$ .

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Step 3.1

Rewrite $36$ as $6^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 6$ and $b = y - 2$ .

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

Step 3.3

Simplify.

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Step 3.3.1

Subtract $2$ from $6$ .

$x = \pm \sqrt{(y + 4) (6 - (y - 2))}$

Step 3.3.2

Apply the distributive property.

$x = \pm \sqrt{(y + 4) (6 - y - - 2)}$

Step 3.3.3

Multiply $- 1$ by $- 2$ .

$x = \pm \sqrt{(y + 4) (6 - y + 2)}$

Step 3.3.4

Add $6$ and $2$ .

$x = \pm \sqrt{(y + 4) (- y + 8)}$

Step 4

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

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Step 4.1

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

$x = \sqrt{(y + 4) (- y + 8)}$

Step 4.2

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

$x = - \sqrt{(y + 4) (- y + 8)}$

Step 4.3

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

$x = \sqrt{(y + 4) (- y + 8)}$

$x = - \sqrt{(y + 4) (- y + 8)}$

$x = \sqrt{(y + 4) (- y + 8)}$

$x = - \sqrt{(y + 4) (- y + 8)}$