Find the Domain -2x^2-6y=-2x+5y

$- 2 x^{2} - 6 y = - 2 x + 5 y$

Step 1

Move all terms containing $y$ to the left side of the equation.

Subtract $5 y$ from both sides of the equation.

$- 2 x^{2} - 6 y - 5 y = - 2 x$

Subtract $5 y$ from $- 6 y$ .

$- 2 x^{2} - 11 y = - 2 x$

Step 2

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

$- 11 y = - 2 x + 2 x^{2}$

Step 3

Divide each term in $- 11 y = - 2 x + 2 x^{2}$ by $- 11$ and simplify.

Divide each term in $- 11 y = - 2 x + 2 x^{2}$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{- 2 x}{- 11} + \frac{2 x^{2}}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{- 2 x}{- 11} + \frac{2 x^{2}}{- 11}$

Divide $y$ by $1$ .

$y = \frac{- 2 x}{- 11} + \frac{2 x^{2}}{- 11}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{(2) x}{11} + \frac{2 x^{2}}{- 11}$

Move the negative in front of the fraction.

$y = \frac{2 x}{11} - \frac{2 x^{2}}{11}$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 5

Find the Domain -2x^2-6y=-2x+5y

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