Algebra Examples

$y = - \frac{1}{14} (x - 3) (x - 8)$

Step 1

Solve the equation for $y$ .

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Step 1.1

Remove parentheses.

$y = - \frac{1}{14} \cdot ((x - 3) (x - 8))$

Step 1.2

Remove parentheses.

$y = - \frac{1}{14} \cdot ((x - 3) (x - 8))$

Step 1.3

Simplify $- \frac{1}{14} \cdot ((x - 3) (x - 8))$ .

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Step 1.3.1

Expand $(x - 3) (x - 8)$ using the FOIL Method.

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Step 1.3.1.1

Apply the distributive property.

$y = - \frac{1}{14} \cdot (x (x - 8) - 3 (x - 8))$

Step 1.3.1.2

Apply the distributive property.

$y = - \frac{1}{14} \cdot (x \cdot x + x \cdot - 8 - 3 (x - 8))$

Step 1.3.1.3

Apply the distributive property.

$y = - \frac{1}{14} \cdot (x \cdot x + x \cdot - 8 - 3 x - 3 \cdot - 8)$

Step 1.3.2

Simplify and combine like terms.

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Step 1.3.2.1

Simplify each term.

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Step 1.3.2.1.1

Multiply $x$ by $x$ .

$y = - \frac{1}{14} \cdot (x^{2} + x \cdot - 8 - 3 x - 3 \cdot - 8)$

Step 1.3.2.1.2

Move $- 8$ to the left of $x$ .

$y = - \frac{1}{14} \cdot (x^{2} - 8 \cdot x - 3 x - 3 \cdot - 8)$

Step 1.3.2.1.3

Multiply $- 3$ by $- 8$ .

$y = - \frac{1}{14} \cdot (x^{2} - 8 x - 3 x + 24)$

Step 1.3.2.2

Subtract $3 x$ from $- 8 x$ .

$y = - \frac{1}{14} \cdot (x^{2} - 11 x + 24)$

Step 1.3.3

Apply the distributive property.

$y = - \frac{1}{14} x^{2} - \frac{1}{14} (- 11 x) - \frac{1}{14} \cdot 24$

Step 1.3.4

Simplify.

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Step 1.3.4.1

Combine $x^{2}$ and $\frac{1}{14}$ .

$y = - \frac{x^{2}}{14} - \frac{1}{14} (- 11 x) - \frac{1}{14} \cdot 24$

Step 1.3.4.2

Multiply $- \frac{1}{14} (- 11 x)$ .

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Step 1.3.4.2.1

Multiply $- 11$ by $- 1$ .

$y = - \frac{x^{2}}{14} + 11 (\frac{1}{14}) x - \frac{1}{14} \cdot 24$

Step 1.3.4.2.2

Combine $11$ and $\frac{1}{14}$ .

$y = - \frac{x^{2}}{14} + \frac{11}{14} x - \frac{1}{14} \cdot 24$

Step 1.3.4.2.3

Combine $\frac{11}{14}$ and $x$ .

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} - \frac{1}{14} \cdot 24$

Step 1.3.4.3

Cancel the common factor of $2$ .

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Step 1.3.4.3.1

Move the leading negative in $- \frac{1}{14}$ into the numerator.

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} + \frac{- 1}{14} \cdot 24$

Step 1.3.4.3.2

Factor $2$ out of $14$ .

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} + \frac{- 1}{2 (7)} \cdot 24$

Step 1.3.4.3.3

Factor $2$ out of $24$ .

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} + \frac{- 1}{2 \cdot 7} \cdot (2 \cdot 12)$

Step 1.3.4.3.4

Cancel the common factor.

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} + \frac{- 1}{2 \cdot 7} \cdot (2 \cdot 12)$

Step 1.3.4.3.5

Rewrite the expression.

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} + \frac{- 1}{7} \cdot 12$

Step 1.3.4.4

Combine $\frac{- 1}{7}$ and $12$ .

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} + \frac{- 1 \cdot 12}{7}$

Step 1.3.4.5

Multiply $- 1$ by $12$ .

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} + \frac{- 12}{7}$

Step 1.3.5

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{14} + \frac{11 x}{14} - \frac{12}{7}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = - \frac{0^{2}}{14} + \frac{11 (0)}{14} - \frac{12}{7}$

Step 3.2

Remove parentheses.

$y = - \frac{{(0)}^{2}}{14} + \frac{11 (0)}{14} - \frac{12}{7}$

Step 3.3

Simplify $- \frac{{(0)}^{2}}{14} + \frac{11 (0)}{14} - \frac{12}{7}$ .

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Step 3.3.1

Combine the numerators over the common denominator.

$y = \frac{- {(0)}^{2} + 11 (0)}{14} + \frac{- 12}{7}$

Step 3.3.2

Simplify each term.

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Step 3.3.2.1

Raising $0$ to any positive power yields $0$ .

$y = \frac{- 0 + 11 (0)}{14} + \frac{- 12}{7}$

Step 3.3.2.2

Multiply $- 1$ by $0$ .

$y = \frac{0 + 11 (0)}{14} + \frac{- 12}{7}$

Step 3.3.2.3

Multiply $11$ by $0$ .

$y = \frac{0 + 0}{14} + \frac{- 12}{7}$

Step 3.3.3

Add $0$ and $0$ .

$y = \frac{0}{14} + \frac{- 12}{7}$

Step 3.3.4

Simplify each term.

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Step 3.3.4.1

Divide $0$ by $14$ .

$y = 0 + \frac{- 12}{7}$

Step 3.3.4.2

Move the negative in front of the fraction.

$y = 0 - \frac{12}{7}$

Step 3.3.5

Subtract $\frac{12}{7}$ from $0$ .

$y = - \frac{12}{7}$

Step 3.4

Use the $x$ and $y$ values to form the ordered pair.

$(0, - \frac{12}{7})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - \frac{1^{2}}{14} + \frac{11 (1)}{14} - \frac{12}{7}$

Step 4.2

Remove parentheses.

$y = - \frac{{(1)}^{2}}{14} + \frac{11 (1)}{14} - \frac{12}{7}$

Step 4.3

Simplify $- \frac{{(1)}^{2}}{14} + \frac{11 (1)}{14} - \frac{12}{7}$ .

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Step 4.3.1

Combine the numerators over the common denominator.

$y = \frac{- {(1)}^{2} + 11 (1)}{14} + \frac{- 12}{7}$

Step 4.3.2

Simplify each term.

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Step 4.3.2.1

One to any power is one.

$y = \frac{- 1 \cdot 1 + 11 (1)}{14} + \frac{- 12}{7}$

Step 4.3.2.2

Multiply $- 1$ by $1$ .

$y = \frac{- 1 + 11 (1)}{14} + \frac{- 12}{7}$

Step 4.3.2.3

Multiply $11$ by $1$ .

$y = \frac{- 1 + 11}{14} + \frac{- 12}{7}$

Step 4.3.3

Add $- 1$ and $11$ .

$y = \frac{10}{14} + \frac{- 12}{7}$

Step 4.3.4

Simplify each term.

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Step 4.3.4.1

Cancel the common factor of $10$ and $14$ .

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Step 4.3.4.1.1

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{14} + \frac{- 12}{7}$

Step 4.3.4.1.2

Cancel the common factors.

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Step 4.3.4.1.2.1

Factor $2$ out of $14$ .

$y = \frac{2 \cdot 5}{2 \cdot 7} + \frac{- 12}{7}$

Step 4.3.4.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot 7} + \frac{- 12}{7}$

Step 4.3.4.1.2.3

Rewrite the expression.

$y = \frac{5}{7} + \frac{- 12}{7}$

Step 4.3.4.2

Move the negative in front of the fraction.

$y = \frac{5}{7} - \frac{12}{7}$

Step 4.3.5

Combine fractions.

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Step 4.3.5.1

Combine the numerators over the common denominator.

$y = \frac{5 - 12}{7}$

Step 4.3.5.2

Simplify the expression.

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Step 4.3.5.2.1

Subtract $12$ from $5$ .

$y = \frac{- 7}{7}$

Step 4.3.5.2.2

Divide $- 7$ by $7$ .

$y = - 1$

Step 4.4

Use the $x$ and $y$ values to form the ordered pair.

$(1, - 1)$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - \frac{2^{2}}{14} + \frac{11 (2)}{14} - \frac{12}{7}$

Step 5.2

Remove parentheses.

$y = - \frac{{(2)}^{2}}{14} + \frac{11 (2)}{14} - \frac{12}{7}$

Step 5.3

Simplify $- \frac{{(2)}^{2}}{14} + \frac{11 (2)}{14} - \frac{12}{7}$ .

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Step 5.3.1

Combine the numerators over the common denominator.

$y = \frac{- {(2)}^{2} + 11 (2)}{14} + \frac{- 12}{7}$

Step 5.3.2

Simplify each term.

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Step 5.3.2.1

Raise $2$ to the power of $2$ .

$y = \frac{- 1 \cdot 4 + 11 (2)}{14} + \frac{- 12}{7}$

Step 5.3.2.2

Multiply $- 1$ by $4$ .

$y = \frac{- 4 + 11 (2)}{14} + \frac{- 12}{7}$

Step 5.3.2.3

Multiply $11$ by $2$ .

$y = \frac{- 4 + 22}{14} + \frac{- 12}{7}$

Step 5.3.3

Add $- 4$ and $22$ .

$y = \frac{18}{14} + \frac{- 12}{7}$

Step 5.3.4

Simplify each term.

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Step 5.3.4.1

Cancel the common factor of $18$ and $14$ .

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Step 5.3.4.1.1

Factor $2$ out of $18$ .

$y = \frac{2 (9)}{14} + \frac{- 12}{7}$

Step 5.3.4.1.2

Cancel the common factors.

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Step 5.3.4.1.2.1

Factor $2$ out of $14$ .

$y = \frac{2 \cdot 9}{2 \cdot 7} + \frac{- 12}{7}$

Step 5.3.4.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 9}{2 \cdot 7} + \frac{- 12}{7}$

Step 5.3.4.1.2.3

Rewrite the expression.

$y = \frac{9}{7} + \frac{- 12}{7}$

Step 5.3.4.2

Move the negative in front of the fraction.

$y = \frac{9}{7} - \frac{12}{7}$

Step 5.3.5

Combine fractions.

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Step 5.3.5.1

Combine the numerators over the common denominator.

$y = \frac{9 - 12}{7}$

Step 5.3.5.2

Simplify the expression.

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Step 5.3.5.2.1

Subtract $12$ from $9$ .

$y = \frac{- 3}{7}$

Step 5.3.5.2.2

Move the negative in front of the fraction.

$y = - \frac{3}{7}$

Step 5.4

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{3}{7})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{12}{7}), (1, - 1), (2, - \frac{3}{7})$

Step 7