Finite Math Examples

$4 x^{2} + 4 y^{2} = 64$

Step 1

Subtract $4 x^{2}$ from both sides of the equation.

$4 y^{2} = 64 - 4 x^{2}$

Step 2

Divide each term in $4 y^{2} = 64 - 4 x^{2}$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y^{2} = 64 - 4 x^{2}$ by $4$ .

$\frac{4 y^{2}}{4} = \frac{64}{4} + \frac{- 4 x^{2}}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 y^{2}}{4} = \frac{64}{4} + \frac{- 4 x^{2}}{4}$

Step 2.2.1.2

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

$y^{2} = \frac{64}{4} + \frac{- 4 x^{2}}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $64$ by $4$ .

$y^{2} = 16 + \frac{- 4 x^{2}}{4}$

Step 2.3.1.2

Cancel the common factor of $- 4$ and $4$ .

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Step 2.3.1.2.1

Factor $4$ out of $- 4 x^{2}$ .

$y^{2} = 16 + \frac{4 (- x^{2})}{4}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $4$ out of $4$ .

$y^{2} = 16 + \frac{4 (- x^{2})}{4 (1)}$

Step 2.3.1.2.2.2

Cancel the common factor.

$y^{2} = 16 + \frac{4 (- x^{2})}{4 \cdot 1}$

Step 2.3.1.2.2.3

Rewrite the expression.

$y^{2} = 16 + \frac{- x^{2}}{1}$

Step 2.3.1.2.2.4

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

$y^{2} = 16 - x^{2}$

Step 3

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

$y = \pm \sqrt{16 - x^{2}}$

Step 4

Simplify $\pm \sqrt{16 - x^{2}}$ .

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Step 4.1

Rewrite $16$ as $4^{2}$ .

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

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = x$ .

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

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.

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

Step 5.2

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

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

Step 5.3

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

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

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

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

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