Trigonometry Examples

$x^{2} + y + 6 x - 4 y = 23$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $4 y$ from $y$ .

$x^{2} + 6 x - 3 y = 23$

Step 1.2

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

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Step 1.2.1

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

$6 x - 3 y = 23 - x^{2}$

Step 1.2.2

Subtract $6 x$ from both sides of the equation.

$- 3 y = 23 - x^{2} - 6 x$

Step 1.3

Divide each term in $- 3 y = 23 - x^{2} - 6 x$ by $- 3$ and simplify.

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Step 1.3.1

Divide each term in $- 3 y = 23 - x^{2} - 6 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{23}{- 3} + \frac{- x^{2}}{- 3} + \frac{- 6 x}{- 3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{23}{- 3} + \frac{- x^{2}}{- 3} + \frac{- 6 x}{- 3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{23}{- 3} + \frac{- x^{2}}{- 3} + \frac{- 6 x}{- 3}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{23}{3} + \frac{- x^{2}}{- 3} + \frac{- 6 x}{- 3}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{23}{3} + \frac{x^{2}}{3} + \frac{- 6 x}{- 3}$

Step 1.3.3.1.3

Cancel the common factor of $- 6$ and $- 3$ .

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Step 1.3.3.1.3.1

Factor $- 3$ out of $- 6 x$ .

$y = - \frac{23}{3} + \frac{x^{2}}{3} + \frac{- 3 (2 x)}{- 3}$

Step 1.3.3.1.3.2

Cancel the common factors.

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Step 1.3.3.1.3.2.1

Factor $- 3$ out of $- 3$ .

$y = - \frac{23}{3} + \frac{x^{2}}{3} + \frac{- 3 (2 x)}{- 3 (1)}$

Step 1.3.3.1.3.2.2

Cancel the common factor.

$y = - \frac{23}{3} + \frac{x^{2}}{3} + \frac{- 3 (2 x)}{- 3 \cdot 1}$

Step 1.3.3.1.3.2.3

Rewrite the expression.

$y = - \frac{23}{3} + \frac{x^{2}}{3} + \frac{2 x}{1}$

Step 1.3.3.1.3.2.4

Divide $2 x$ by $1$ .

$y = - \frac{23}{3} + \frac{x^{2}}{3} + 2 x$

Step 2

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.