Calculus Examples

$9 x^{2} - y^{2} = 8$

Step 1

Subtract $9 x^{2}$ from both sides of the equation.

$- y^{2} = 8 - 9 x^{2}$

Step 2

Divide each term in $- y^{2} = 8 - 9 x^{2}$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- y^{2} = 8 - 9 x^{2}$ by $- 1$ .

$\frac{- y^{2}}{- 1} = \frac{8}{- 1} + \frac{- 9 x^{2}}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{y^{2}}{1} = \frac{8}{- 1} + \frac{- 9 x^{2}}{- 1}$

Step 2.2.2

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

$y^{2} = \frac{8}{- 1} + \frac{- 9 x^{2}}{- 1}$

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 $8$ by $- 1$ .

$y^{2} = - 8 + \frac{- 9 x^{2}}{- 1}$

Step 2.3.1.2

Move the negative one from the denominator of $\frac{- 9 x^{2}}{- 1}$ .

$y^{2} = - 8 - 1 \cdot (- 9 x^{2})$

Step 2.3.1.3

Rewrite $- 1 \cdot (- 9 x^{2})$ as $- (- 9 x^{2})$ .

$y^{2} = - 8 - (- 9 x^{2})$

Step 2.3.1.4

Multiply $- 9$ by $- 1$ .

$y^{2} = - 8 + 9 x^{2}$

Step 3

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

$y = \pm \sqrt{- 8 + 9 x^{2}}$

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.

$y = \sqrt{- 8 + 9 x^{2}}$

Step 4.2

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

$y = - \sqrt{- 8 + 9 x^{2}}$

Step 4.3

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

$y = \sqrt{- 8 + 9 x^{2}}$

$y = - \sqrt{- 8 + 9 x^{2}}$

$y = \sqrt{- 8 + 9 x^{2}}$

$y = - \sqrt{- 8 + 9 x^{2}}$