Write as a Function of x x^2+y=-2x-y

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

Step 1

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

Add $y$ to both sides of the equation.

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

Add $y$ and $y$ .

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

Step 2

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

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

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 x$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

$y = \frac{2 (- x)}{2 \cdot 1} + \frac{- x^{2}}{2}$

Rewrite the expression.

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

Divide $- x$ by $1$ .

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

Move the negative in front of the fraction.

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

Step 4

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = - x - \frac{x^{2}}{2}$

Write as a Function of x x^2+y=-2x-y

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