Algebra Examples

$5 x^{2} + y = 3 x + 3 y$

Step 1

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

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Step 1.1

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

$5 x^{2} + y - 3 y = 3 x$

Step 1.2

Subtract $3 y$ from $y$ .

$5 x^{2} - 2 y = 3 x$

Step 2

Subtract $5 x^{2}$ from both sides of the equation.

$- 2 y = 3 x - 5 x^{2}$

Step 3

Divide each term in $- 2 y = 3 x - 5 x^{2}$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 y = 3 x - 5 x^{2}$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{3 x}{- 2} + \frac{- 5 x^{2}}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{3 x}{- 2} + \frac{- 5 x^{2}}{- 2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{3 x}{- 2} + \frac{- 5 x^{2}}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{3 x}{2} + \frac{- 5 x^{2}}{- 2}$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{3 x}{2} + \frac{5 x^{2}}{2}$

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.

$f (x) = - \frac{3 x}{2} + \frac{5 x^{2}}{2}$