Precalculus Examples

$x^{2} - 4 x - 8 y + 28 = 0$

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.

$- 4 x - 8 y + 28 = - x^{2}$

Step 1.1.2

Add $4 x$ to both sides of the equation.

$- 8 y + 28 = - x^{2} + 4 x$

Step 1.1.3

Subtract $28$ from both sides of the equation.

$- 8 y = - x^{2} + 4 x - 28$

Step 1.2

Divide each term in $- 8 y = - x^{2} + 4 x - 28$ by $- 8$ and simplify.

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Step 1.2.1

Divide each term in $- 8 y = - x^{2} + 4 x - 28$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- x^{2}}{- 8} + \frac{4 x}{- 8} + \frac{- 28}{- 8}$

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.

$\frac{- 8 y}{- 8} = \frac{- x^{2}}{- 8} + \frac{4 x}{- 8} + \frac{- 28}{- 8}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x^{2}}{- 8} + \frac{4 x}{- 8} + \frac{- 28}{- 8}$

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.

$y = \frac{x^{2}}{8} + \frac{4 x}{- 8} + \frac{- 28}{- 8}$

Step 1.2.3.1.2

Cancel the common factor of $4$ and $- 8$ .

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Step 1.2.3.1.2.1

Factor $4$ out of $4 x$ .

$y = \frac{x^{2}}{8} + \frac{4 (x)}{- 8} + \frac{- 28}{- 8}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $4$ out of $- 8$ .

$y = \frac{x^{2}}{8} + \frac{4 x}{4 \cdot - 2} + \frac{- 28}{- 8}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{x^{2}}{8} + \frac{4 x}{4 \cdot - 2} + \frac{- 28}{- 8}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{x^{2}}{8} + \frac{x}{- 2} + \frac{- 28}{- 8}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y = \frac{x^{2}}{8} - \frac{x}{2} + \frac{- 28}{- 8}$

Step 1.2.3.1.4

Cancel the common factor of $- 28$ and $- 8$ .

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Step 1.2.3.1.4.1

Factor $- 4$ out of $- 28$ .

$y = \frac{x^{2}}{8} - \frac{x}{2} + \frac{- 4 (7)}{- 8}$

Step 1.2.3.1.4.2

Cancel the common factors.

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Step 1.2.3.1.4.2.1

Factor $- 4$ out of $- 8$ .

$y = \frac{x^{2}}{8} - \frac{x}{2} + \frac{- 4 \cdot 7}{- 4 \cdot 2}$

Step 1.2.3.1.4.2.2

Cancel the common factor.

$y = \frac{x^{2}}{8} - \frac{x}{2} + \frac{- 4 \cdot 7}{- 4 \cdot 2}$

Step 1.2.3.1.4.2.3

Rewrite the expression.

$y = \frac{x^{2}}{8} - \frac{x}{2} + \frac{7}{2}$

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.

$y = \frac{1}{8} x^{2} - (\frac{1}{2} x) + \frac{7}{2}$

Step 4

Remove parentheses.

$y = \frac{1}{8} x^{2} - \frac{1}{2} x + \frac{7}{2}$

Step 5