Write as a Function of x x^2+2y=-2x+3y

$x^{2} + 2 y = - 2 x + 3 y$

Step 1

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

Subtract $3 y$ from both sides of the equation.

$x^{2} + 2 y - 3 y = - 2 x$

Subtract $3 y$ from $2 y$ .

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

Step 2

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

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

Step 3

Divide each term in $- y = - 2 x - x^{2}$ by $- 1$ and simplify.

Divide each term in $- y = - 2 x - x^{2}$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

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

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

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

Multiply $- 2$ by $- 1$ .

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

Dividing two negative values results in a positive value.

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

Divide $x^{2}$ by $1$ .

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

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.

$f (x) = 2 x + x^{2}$

Write as a Function of x x^2+2y=-2x+3y

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