Precalculus Examples

$x^{2} + y^{2} + a x + b y + c = 0$

Step 1

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

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Step 1.1

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

$y^{2} + a x + b y + c = - x^{2}$

Step 1.2

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

$a x + b y + c = - x^{2} - y^{2}$

Step 1.3

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

$a x + c = - x^{2} - y^{2} - b y$

Step 1.4

Subtract $c$ from both sides of the equation.

$a x = - x^{2} - y^{2} - b y - c$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $x$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $a$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $x^{2}$ and $x$ .

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Step 2.3.1.1.1

Factor $x$ out of $- x^{2}$ .

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

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Raise $x$ to the power of $1$ .

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

Step 2.3.1.1.2.2

Factor $x$ out of $x^{1}$ .

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

Step 2.3.1.1.2.3

Cancel the common factor.

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

Step 2.3.1.1.2.4

Rewrite the expression.

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

Step 2.3.1.1.2.5

Divide $- x$ by $1$ .

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

Step 2.3.1.2

Move the negative in front of the fraction.

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

Step 2.3.1.3

Move the negative in front of the fraction.

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

Step 2.3.1.4

Move the negative in front of the fraction.

$a = - x - \frac{y^{2}}{x} - \frac{b y}{x} - \frac{c}{x}$