Find the Domain -x^2+2x-4y=-2y

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

Step 1

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

Add $2 y$ to both sides of the equation.

$- x^{2} + 2 x - 4 y + 2 y = 0$

Add $- 4 y$ and $2 y$ .

$- x^{2} + 2 x - 2 y = 0$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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

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

Subtract $2 x$ from both sides of the equation.

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

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

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 -x^2+2x-4y=-2y

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