Algebra Examples

2 x^{2} - 2 y^{2} + 5 = 9

$2 x^{2} - 2 y^{2} + 5 = 9$

Step 1

Move all terms not containing a variable to the right side of the equation.

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Step 1.1

Subtract

5

$5$ from both sides of the equation.

2 x^{2} - 2 y^{2} = 9 - 5

$2 x^{2} - 2 y^{2} = 9 - 5$

Step 1.2

Subtract

5

$5$ from

9

$9$ .

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

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

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

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

Step 2

Divide each term by

4

$4$ to make the right side equal to one.

\frac{2 x^{2}}{4} - \frac{2 y^{2}}{4} = \frac{4}{4}

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

Step 3

Simplify each term in the equation in order to set the right side equal to

1

$1$ . The standard form of an ellipse or hyperbola requires the right side of the equation be

1

$1$ .

\frac{x^{2}}{2} - \frac{y^{2}}{2} = 1

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

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