Precalculus Examples

$x^{2} - 6 x - 8 y - 31 = 0$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

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

$- 6 x - 8 y - 31 = - x^{2}$

Step 1.1.2

Add $6 x$ to both sides of the equation.

$- 8 y - 31 = - x^{2} + 6 x$

Step 1.1.3

Add $31$ to both sides of the equation.

$- 8 y = - x^{2} + 6 x + 31$

Step 1.2

Divide each term in $- 8 y = - x^{2} + 6 x + 31$ by $- 8$ and simplify.

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Step 1.2.1

Divide each term in $- 8 y = - x^{2} + 6 x + 31$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- x^{2}}{- 8} + \frac{6 x}{- 8} + \frac{31}{- 8}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- x^{2}}{- 8} + \frac{6 x}{- 8} + \frac{31}{- 8}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x^{2}}{- 8} + \frac{6 x}{- 8} + \frac{31}{- 8}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{x^{2}}{8} + \frac{6 x}{- 8} + \frac{31}{- 8}$

Step 1.2.3.1.2

Cancel the common factor of $6$ and $- 8$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $6 x$ .

$y = \frac{x^{2}}{8} + \frac{2 (3 x)}{- 8} + \frac{31}{- 8}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $- 8$ .

$y = \frac{x^{2}}{8} + \frac{2 (3 x)}{2 (- 4)} + \frac{31}{- 8}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{x^{2}}{8} + \frac{2 (3 x)}{2 \cdot - 4} + \frac{31}{- 8}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{x^{2}}{8} + \frac{3 x}{- 4} + \frac{31}{- 8}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y = \frac{x^{2}}{8} - \frac{3 x}{4} + \frac{31}{- 8}$

Step 1.2.3.1.4

Move the negative in front of the fraction.

$y = \frac{x^{2}}{8} - \frac{3 x}{4} - \frac{31}{8}$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

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

Step 3

Reorder terms.

$y = \frac{1}{8} x^{2} - (\frac{3}{4} x) - \frac{31}{8}$

Step 4

Remove parentheses.

$y = \frac{1}{8} x^{2} - \frac{3}{4} x - \frac{31}{8}$

Step 5