Precalculus Examples

$- \frac{1}{3} x + y = - \frac{5}{3}$ , $x^{2} + y^{2} = 25$

Step 1

Solve for $y$ in $- \frac{1}{3} x + y = - \frac{5}{3}$ .

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Step 1.1

Combine $x$ and $\frac{1}{3}$ .

$- \frac{x}{3} + y = - \frac{5}{3}$

$x^{2} + y^{2} = 25$

Step 1.2

Add $\frac{x}{3}$ to both sides of the equation.

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + y^{2} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + y^{2} = 25$

Step 2

Replace all occurrences of $y$ with $- \frac{5}{3} + \frac{x}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $x^{2} + y^{2} = 25$ with $- \frac{5}{3} + \frac{x}{3}$ .

$x^{2} + {(- \frac{5}{3} + \frac{x}{3})}^{2} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x^{2} + {(- \frac{5}{3} + \frac{x}{3})}^{2}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Rewrite ${(- \frac{5}{3} + \frac{x}{3})}^{2}$ as $(- \frac{5}{3} + \frac{x}{3}) (- \frac{5}{3} + \frac{x}{3})$ .

$x^{2} + (- \frac{5}{3} + \frac{x}{3}) (- \frac{5}{3} + \frac{x}{3}) = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.2

Expand $(- \frac{5}{3} + \frac{x}{3}) (- \frac{5}{3} + \frac{x}{3})$ using the FOIL Method.

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Step 2.2.1.1.2.1

Apply the distributive property.

$x^{2} - \frac{5}{3} \cdot (- \frac{5}{3} + \frac{x}{3}) + \frac{x}{3} \cdot (- \frac{5}{3} + \frac{x}{3}) = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.2.2

Apply the distributive property.

$x^{2} - \frac{5}{3} \cdot (- \frac{5}{3}) - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3} + \frac{x}{3}) = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.2.3

Apply the distributive property.

$x^{2} - \frac{5}{3} \cdot (- \frac{5}{3}) - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} - \frac{5}{3} \cdot (- \frac{5}{3}) - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3

Simplify and combine like terms.

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Step 2.2.1.1.3.1

Simplify each term.

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Step 2.2.1.1.3.1.1

Multiply $- \frac{5}{3} (- \frac{5}{3})$ .

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Step 2.2.1.1.3.1.1.1

Multiply $- 1$ by $- 1$ .

$x^{2} + 1 (\frac{5}{3}) \cdot \frac{5}{3} - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.1.2

Multiply $\frac{5}{3}$ by $1$ .

$x^{2} + \frac{5}{3} \cdot \frac{5}{3} - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.1.3

Multiply $\frac{5}{3}$ by $\frac{5}{3}$ .

$x^{2} + \frac{5 \cdot 5}{3 \cdot 3} - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.1.4

Multiply $5$ by $5$ .

$x^{2} + \frac{25}{3 \cdot 3} - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.1.5

Multiply $3$ by $3$ .

$x^{2} + \frac{25}{9} - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - \frac{5}{3} \cdot \frac{x}{3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.2

Multiply $- \frac{5}{3} \cdot \frac{x}{3}$ .

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Step 2.2.1.1.3.1.2.1

Multiply $\frac{x}{3}$ by $\frac{5}{3}$ .

$x^{2} + \frac{25}{9} - \frac{x \cdot 5}{3 \cdot 3} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.2.2

Multiply $3$ by $3$ .

$x^{2} + \frac{25}{9} - \frac{x \cdot 5}{9} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - \frac{x \cdot 5}{9} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.3

Move $5$ to the left of $x$ .

$x^{2} + \frac{25}{9} - \frac{5 \cdot x}{9} + \frac{x}{3} \cdot (- \frac{5}{3}) + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.4

Multiply $\frac{x}{3} (- \frac{5}{3})$ .

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Step 2.2.1.1.3.1.4.1

Multiply $\frac{x}{3}$ by $\frac{5}{3}$ .

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{x \cdot 5}{3 \cdot 3} + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.4.2

Multiply $3$ by $3$ .

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{x \cdot 5}{9} + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{x \cdot 5}{9} + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.5

Move $5$ to the left of $x$ .

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 \cdot x}{9} + \frac{x}{3} \cdot \frac{x}{3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.6

Multiply $\frac{x}{3} \cdot \frac{x}{3}$ .

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Step 2.2.1.1.3.1.6.1

Multiply $\frac{x}{3}$ by $\frac{x}{3}$ .

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x \cdot x}{3 \cdot 3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.6.2

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

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x \cdot x}{3 \cdot 3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.6.3

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

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x \cdot x}{3 \cdot 3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x^{1 + 1}}{3 \cdot 3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.6.5

Add $1$ and $1$ .

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x^{2}}{3 \cdot 3} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.1.6.6

Multiply $3$ by $3$ .

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - \frac{5 x}{9} - \frac{5 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.3.2

Subtract $\frac{5 x}{9}$ from $- \frac{5 x}{9}$ .

$x^{2} + \frac{25}{9} - 2 \frac{5 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - 2 \frac{5 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.4

Simplify each term.

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Step 2.2.1.1.4.1

Multiply $- 2 \frac{5 x}{9}$ .

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Step 2.2.1.1.4.1.1

Combine $- 2$ and $\frac{5 x}{9}$ .

$x^{2} + \frac{25}{9} + \frac{- 2 (5 x)}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.4.1.2

Multiply $5$ by $- 2$ .

$x^{2} + \frac{25}{9} + \frac{- 10 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} + \frac{- 10 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.1.4.2

Move the negative in front of the fraction.

$x^{2} + \frac{25}{9} - \frac{10 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - \frac{10 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$x^{2} + \frac{25}{9} - \frac{10 x}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.2

To write $x^{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{25}{9} - \frac{10 x}{9} + x^{2} \cdot \frac{9}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.3

Simplify terms.

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Step 2.2.1.3.1

Combine $x^{2}$ and $\frac{9}{9}$ .

$\frac{25}{9} - \frac{10 x}{9} + \frac{x^{2} \cdot 9}{9} + \frac{x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.3.2

Combine the numerators over the common denominator.

$\frac{25}{9} - \frac{10 x}{9} + \frac{x^{2} \cdot 9 + x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.3.3

Combine the numerators over the common denominator.

$\frac{25 - 10 x + x^{2} \cdot 9 + x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$\frac{25 - 10 x + x^{2} \cdot 9 + x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.4

Move $9$ to the left of $x^{2}$ .

$\frac{25 - 10 x + 9 x^{2} + x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.5

Simplify terms.

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Step 2.2.1.5.1

Add $9 x^{2}$ and $x^{2}$ .

$\frac{25 - 10 x + 10 x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.5.2

Factor $5$ out of $25 - 10 x + 10 x^{2}$ .

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Step 2.2.1.5.2.1

Factor $5$ out of $25$ .

$\frac{5 (5) - 10 x + 10 x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.5.2.2

Factor $5$ out of $- 10 x$ .

$\frac{5 (5) + 5 (- 2 x) + 10 x^{2}}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.5.2.3

Factor $5$ out of $10 x^{2}$ .

$\frac{5 (5) + 5 (- 2 x) + 5 (2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.5.2.4

Factor $5$ out of $5 (5) + 5 (- 2 x)$ .

$\frac{5 (5 - 2 x) + 5 (2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 2.2.1.5.2.5

Factor $5$ out of $5 (5 - 2 x) + 5 (2 x^{2})$ .

$\frac{5 (5 - 2 x + 2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$\frac{5 (5 - 2 x + 2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$\frac{5 (5 - 2 x + 2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$\frac{5 (5 - 2 x + 2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$\frac{5 (5 - 2 x + 2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

$\frac{5 (5 - 2 x + 2 x^{2})}{9} = 25$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3

Solve for $x$ in $\frac{5 (5 - 2 x + 2 x^{2})}{9} = 25$ .

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Step 3.1

Multiply both sides by $9$ .

$\frac{5 (5 - 2 x + 2 x^{2})}{9} \cdot 9 = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $\frac{5 (5 - 2 x + 2 x^{2})}{9} \cdot 9$ .

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Step 3.2.1.1.1

Cancel the common factor of $9$ .

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Step 3.2.1.1.1.1

Cancel the common factor.

$\frac{5 (5 - 2 x + 2 x^{2})}{9} \cdot 9 = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.1.1.1.2

Rewrite the expression.

$5 (5 - 2 x + 2 x^{2}) = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

$5 (5 - 2 x + 2 x^{2}) = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.1.1.2

Apply the distributive property.

$5 \cdot 5 + 5 (- 2 x) + 5 (2 x^{2}) = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.1.1.3

Simplify.

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Step 3.2.1.1.3.1

Multiply $5$ by $5$ .

$25 + 5 (- 2 x) + 5 (2 x^{2}) = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.1.1.3.2

Multiply $- 2$ by $5$ .

$25 - 10 x + 5 (2 x^{2}) = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.1.1.3.3

Multiply $2$ by $5$ .

$25 - 10 x + 10 x^{2} = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

$25 - 10 x + 10 x^{2} = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.1.1.4

Move $25$ .

$- 10 x + 10 x^{2} + 25 = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.1.1.5

Reorder $- 10 x$ and $10 x^{2}$ .

$10 x^{2} - 10 x + 25 = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 x^{2} - 10 x + 25 = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 x^{2} - 10 x + 25 = 25 \cdot 9$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $25$ by $9$ .

$10 x^{2} - 10 x + 25 = 225$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 x^{2} - 10 x + 25 = 225$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 x^{2} - 10 x + 25 = 225$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3

Solve for $x$ .

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Step 3.3.1

Subtract $225$ from both sides of the equation.

$10 x^{2} - 10 x + 25 - 225 = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.2

Subtract $225$ from $25$ .

$10 x^{2} - 10 x - 200 = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3

Factor the left side of the equation.

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Step 3.3.3.1

Factor $10$ out of $10 x^{2} - 10 x - 200$ .

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Step 3.3.3.1.1

Factor $10$ out of $10 x^{2}$ .

$10 (x^{2}) - 10 x - 200 = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3.1.2

Factor $10$ out of $- 10 x$ .

$10 (x^{2}) + 10 (- x) - 200 = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3.1.3

Factor $10$ out of $- 200$ .

$10 (x^{2}) + 10 (- x) + 10 (- 20) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3.1.4

Factor $10$ out of $10 (x^{2}) + 10 (- x)$ .

$10 (x^{2} - x) + 10 (- 20) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3.1.5

Factor $10$ out of $10 (x^{2} - x) + 10 (- 20)$ .

$10 (x^{2} - x - 20) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 (x^{2} - x - 20) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3.2

Factor.

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Step 3.3.3.2.1

Factor $x^{2} - x - 20$ using the AC method.

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Step 3.3.3.2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 20$ and whose sum is $- 1$ .

$- 5, 4$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3.2.1.2

Write the factored form using these integers.

$10 ((x - 5) (x + 4)) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 ((x - 5) (x + 4)) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.3.2.2

Remove unnecessary parentheses.

$10 (x - 5) (x + 4) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 (x - 5) (x + 4) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

$10 (x - 5) (x + 4) = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 5 = 0$

$x + 4 = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.5

Set $x - 5$ equal to $0$ and solve for $x$ .

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Step 3.3.5.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.5.2

Add $5$ to both sides of the equation.

$x = 5$

$y = - \frac{5}{3} + \frac{x}{3}$

$x = 5$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.6

Set $x + 4$ equal to $0$ and solve for $x$ .

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Step 3.3.6.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.6.2

Subtract $4$ from both sides of the equation.

$x = - 4$

$y = - \frac{5}{3} + \frac{x}{3}$

$x = - 4$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 3.3.7

The final solution is all the values that make $10 (x - 5) (x + 4) = 0$ true.

$x = 5, - 4$

$y = - \frac{5}{3} + \frac{x}{3}$

$x = 5, - 4$

$y = - \frac{5}{3} + \frac{x}{3}$

$x = 5, - 4$

$y = - \frac{5}{3} + \frac{x}{3}$

Step 4

Replace all occurrences of $x$ with $5$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = - \frac{5}{3} + \frac{x}{3}$ with $5$ .

$y = - \frac{5}{3} + \frac{5}{3}$

$x = 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{5}{3} + \frac{5}{3}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$y = \frac{- 5 + 5}{3}$

$x = 5$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Add $- 5$ and $5$ .

$y = \frac{0}{3}$

$x = 5$

Step 4.2.1.2.2

Divide $0$ by $3$ .

$y = 0$

$x = 5$

$y = 0$

$x = 5$

$y = 0$

$x = 5$

$y = 0$

$x = 5$

$y = 0$

$x = 5$

Step 5

Replace all occurrences of $x$ with $- 4$ in each equation.

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Step 5.1

Replace all occurrences of $x$ in $y = - \frac{5}{3} + \frac{x}{3}$ with $- 4$ .

$y = - \frac{5}{3} + \frac{- 4}{3}$

$x = - 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{5}{3} + \frac{- 4}{3}$ .

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Step 5.2.1.1

Combine the numerators over the common denominator.

$y = \frac{- 5 - 4}{3}$

$x = - 4$

Step 5.2.1.2

Simplify the expression.

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Step 5.2.1.2.1

Subtract $4$ from $- 5$ .

$y = \frac{- 9}{3}$

$x = - 4$

Step 5.2.1.2.2

Divide $- 9$ by $3$ .

$y = - 3$

$x = - 4$

$y = - 3$

$x = - 4$

$y = - 3$

$x = - 4$

$y = - 3$

$x = - 4$

$y = - 3$

$x = - 4$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(5, 0)$

$(- 4, - 3)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(5, 0), (- 4, - 3)$

Equation Form:

$x = 5, y = 0$

$x = - 4, y = - 3$

Step 8