Find the Domain -5x^2-6y=x-4y

$- 5 x^{2} - 6 y = x - 4 y$

Step 1

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

Add $4 y$ to both sides of the equation.

$- 5 x^{2} - 6 y + 4 y = x$

Add $- 6 y$ and $4 y$ .

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

Step 2

Add $5 x^{2}$ to both sides of the equation.

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

Step 3

Divide each term in $- 2 y = x + 5 x^{2}$ by $- 2$ and simplify.

Divide each term in $- 2 y = x + 5 x^{2}$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{x}{- 2} + \frac{5 x^{2}}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{x}{- 2} + \frac{5 x^{2}}{- 2}$

Divide $y$ by $1$ .

$y = \frac{x}{- 2} + \frac{5 x^{2}}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{5 x^{2}}{- 2}$

Move the negative in front of the fraction.

$y = - \frac{x}{2} - \frac{5 x^{2}}{2}$

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 -5x^2-6y=x-4y

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