Precalculus Examples

$x^{2} + y^{2} = 169$ , $x^{2} - 8 y = 104$

Step 1

Solve for $y$ in $x^{2} - 8 y = 104$ .

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Step 1.1

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

$- 8 y = 104 - x^{2}$

$x^{2} + y^{2} = 169$

Step 1.2

Divide each term in $- 8 y = 104 - x^{2}$ by $- 8$ and simplify.

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Step 1.2.1

Divide each term in $- 8 y = 104 - x^{2}$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{104}{- 8} + \frac{- x^{2}}{- 8}$

$x^{2} + y^{2} = 169$

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.

$\frac{- 8 y}{- 8} = \frac{104}{- 8} + \frac{- x^{2}}{- 8}$

$x^{2} + y^{2} = 169$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{104}{- 8} + \frac{- x^{2}}{- 8}$

$x^{2} + y^{2} = 169$

$y = \frac{104}{- 8} + \frac{- x^{2}}{- 8}$

$x^{2} + y^{2} = 169$

$y = \frac{104}{- 8} + \frac{- x^{2}}{- 8}$

$x^{2} + y^{2} = 169$

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

Divide $104$ by $- 8$ .

$y = - 13 + \frac{- x^{2}}{- 8}$

$x^{2} + y^{2} = 169$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + y^{2} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + y^{2} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + y^{2} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + y^{2} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + y^{2} = 169$

Step 2

Replace all occurrences of $y$ with $- 13 + \frac{x^{2}}{8}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $x^{2} + y^{2} = 169$ with $- 13 + \frac{x^{2}}{8}$ .

$x^{2} + {(- 13 + \frac{x^{2}}{8})}^{2} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $x^{2} + {(- 13 + \frac{x^{2}}{8})}^{2}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Rewrite ${(- 13 + \frac{x^{2}}{8})}^{2}$ as $(- 13 + \frac{x^{2}}{8}) (- 13 + \frac{x^{2}}{8})$ .

$x^{2} + (- 13 + \frac{x^{2}}{8}) (- 13 + \frac{x^{2}}{8}) = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.2

Expand $(- 13 + \frac{x^{2}}{8}) (- 13 + \frac{x^{2}}{8})$ using the FOIL Method.

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Step 2.2.1.1.2.1

Apply the distributive property.

$x^{2} - 13 (- 13 + \frac{x^{2}}{8}) + \frac{x^{2}}{8} \cdot (- 13 + \frac{x^{2}}{8}) = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.2.2

Apply the distributive property.

$x^{2} - 13 \cdot - 13 - 13 \frac{x^{2}}{8} + \frac{x^{2}}{8} \cdot (- 13 + \frac{x^{2}}{8}) = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.2.3

Apply the distributive property.

$x^{2} - 13 \cdot - 13 - 13 \frac{x^{2}}{8} + \frac{x^{2}}{8} \cdot - 13 + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} - 13 \cdot - 13 - 13 \frac{x^{2}}{8} + \frac{x^{2}}{8} \cdot - 13 + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

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 $- 13$ by $- 13$ .

$x^{2} + 169 - 13 \frac{x^{2}}{8} + \frac{x^{2}}{8} \cdot - 13 + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.2

Combine $- 13$ and $\frac{x^{2}}{8}$ .

$x^{2} + 169 + \frac{- 13 x^{2}}{8} + \frac{x^{2}}{8} \cdot - 13 + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.3

Move the negative in front of the fraction.

$x^{2} + 169 - \frac{13 x^{2}}{8} + \frac{x^{2}}{8} \cdot - 13 + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.4

Combine $\frac{x^{2}}{8}$ and $- 13$ .

$x^{2} + 169 - \frac{13 x^{2}}{8} + \frac{x^{2} \cdot - 13}{8} + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.5

Move $- 13$ to the left of $x^{2}$ .

$x^{2} + 169 - \frac{13 x^{2}}{8} + \frac{- 13 \cdot x^{2}}{8} + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.6

Move the negative in front of the fraction.

$x^{2} + 169 - \frac{13 x^{2}}{8} - \frac{13 \cdot x^{2}}{8} + \frac{x^{2}}{8} \cdot \frac{x^{2}}{8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.7

Combine.

$x^{2} + 169 - \frac{13 x^{2}}{8} - \frac{13 x^{2}}{8} + \frac{x^{2} x^{2}}{8 \cdot 8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.8

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 2.2.1.1.3.1.8.1

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

$x^{2} + 169 - \frac{13 x^{2}}{8} - \frac{13 x^{2}}{8} + \frac{x^{2 + 2}}{8 \cdot 8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.8.2

Add $2$ and $2$ .

$x^{2} + 169 - \frac{13 x^{2}}{8} - \frac{13 x^{2}}{8} + \frac{x^{4}}{8 \cdot 8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + 169 - \frac{13 x^{2}}{8} - \frac{13 x^{2}}{8} + \frac{x^{4}}{8 \cdot 8} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.1.9

Multiply $8$ by $8$ .

$x^{2} + 169 - \frac{13 x^{2}}{8} - \frac{13 x^{2}}{8} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + 169 - \frac{13 x^{2}}{8} - \frac{13 x^{2}}{8} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.3.2

Subtract $\frac{13 x^{2}}{8}$ from $- \frac{13 x^{2}}{8}$ .

$x^{2} + 169 - 2 \frac{13 x^{2}}{8} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + 169 - 2 \frac{13 x^{2}}{8} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.4

Simplify each term.

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Step 2.2.1.1.4.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.4.1.1

Factor $2$ out of $- 2$ .

$x^{2} + 169 + 2 (- 1) (\frac{13 x^{2}}{8}) + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.4.1.2

Factor $2$ out of $8$ .

$x^{2} + 169 + 2 \cdot (- 1 \frac{13 x^{2}}{2 \cdot 4}) + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.4.1.3

Cancel the common factor.

$x^{2} + 169 + 2 \cdot (- 1 \frac{13 x^{2}}{2 \cdot 4}) + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.4.1.4

Rewrite the expression.

$x^{2} + 169 - 1 \frac{13 x^{2}}{4} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + 169 - 1 \frac{13 x^{2}}{4} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.1.4.2

Rewrite $- 1 \frac{13 x^{2}}{4}$ as $- \frac{13 x^{2}}{4}$ .

$x^{2} + 169 - \frac{13 x^{2}}{4} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + 169 - \frac{13 x^{2}}{4} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$x^{2} + 169 - \frac{13 x^{2}}{4} + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.2

To write $x^{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{2} \cdot \frac{4}{4} - \frac{13 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.3

Combine $x^{2}$ and $\frac{4}{4}$ .

$\frac{x^{2} \cdot 4}{4} - \frac{13 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{x^{2} \cdot 4 - 13 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.5

Subtract $13 x^{2}$ from $x^{2} \cdot 4$ .

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Step 2.2.1.5.1

Reorder $x^{2}$ and $4$ .

$\frac{4 \cdot x^{2} - 13 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.5.2

Subtract $13 x^{2}$ from $4 \cdot x^{2}$ .

$\frac{- 9 \cdot x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$\frac{- 9 \cdot x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 2.2.1.6

Move the negative in front of the fraction.

$- \frac{9 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$- \frac{9 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$- \frac{9 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

$- \frac{9 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$

$y = - 13 + \frac{x^{2}}{8}$

Step 3

Solve for $x$ in $- \frac{9 x^{2}}{4} + 169 + \frac{x^{4}}{64} = 169$ .

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Step 3.1

Substitute $u = x^{2}$ into the equation. This will make the quadratic formula easy to use.

$\frac{u^{2}}{64} - \frac{9 u}{4} + 169 = 169$

$u = x^{2}$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2

Multiply each term in $\frac{u^{2}}{64} - \frac{9 u}{4} + 169 = 169$ by $64$ to eliminate the fractions.

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Step 3.2.1

Multiply each term in $\frac{u^{2}}{64} - \frac{9 u}{4} + 169 = 169$ by $64$ .

$\frac{u^{2}}{64} \cdot 64 - \frac{9 u}{4} \cdot 64 + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Simplify each term.

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Step 3.2.2.1.1

Cancel the common factor of $64$ .

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Step 3.2.2.1.1.1

Cancel the common factor.

$\frac{u^{2}}{64} \cdot 64 - \frac{9 u}{4} \cdot 64 + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2.1.1.2

Rewrite the expression.

$u^{2} - \frac{9 u}{4} \cdot 64 + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

$u^{2} - \frac{9 u}{4} \cdot 64 + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2.1.2

Cancel the common factor of $4$ .

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Step 3.2.2.1.2.1

Move the leading negative in $- \frac{9 u}{4}$ into the numerator.

$u^{2} + \frac{- 9 u}{4} \cdot 64 + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2.1.2.2

Factor $4$ out of $64$ .

$u^{2} + \frac{- 9 u}{4} \cdot (4 (16)) + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2.1.2.3

Cancel the common factor.

$u^{2} + \frac{- 9 u}{4} \cdot (4 \cdot 16) + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2.1.2.4

Rewrite the expression.

$u^{2} - 9 u \cdot 16 + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

$u^{2} - 9 u \cdot 16 + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2.1.3

Multiply $16$ by $- 9$ .

$u^{2} - 144 u + 169 \cdot 64 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.2.1.4

Multiply $169$ by $64$ .

$u^{2} - 144 u + 10816 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

$u^{2} - 144 u + 10816 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

$u^{2} - 144 u + 10816 = 169 \cdot 64$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply $169$ by $64$ .

$u^{2} - 144 u + 10816 = 10816$

$y = - 13 + \frac{x^{2}}{8}$

$u^{2} - 144 u + 10816 = 10816$

$y = - 13 + \frac{x^{2}}{8}$

$u^{2} - 144 u + 10816 = 10816$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.3

Subtract $10816$ from both sides of the equation.

$u^{2} - 144 u + 10816 - 10816 = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.4

Combine the opposite terms in $u^{2} - 144 u + 10816 - 10816$ .

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Step 3.4.1

Subtract $10816$ from $10816$ .

$u^{2} - 144 u + 0 = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.4.2

Add $u^{2} - 144 u$ and $0$ .

$u^{2} - 144 u = 0$

$y = - 13 + \frac{x^{2}}{8}$

$u^{2} - 144 u = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.5

Factor $u$ out of $u^{2} - 144 u$ .

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Step 3.5.1

Factor $u$ out of $u^{2}$ .

$u \cdot u - 144 u = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.5.2

Factor $u$ out of $- 144 u$ .

$u \cdot u + u \cdot - 144 = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.5.3

Factor $u$ out of $u \cdot u + u \cdot - 144$ .

$u (u - 144) = 0$

$y = - 13 + \frac{x^{2}}{8}$

$u (u - 144) = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.6

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

$u = 0$

$u - 144 = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.7

Set $u$ equal to $0$ .

$u = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.8

Set $u - 144$ equal to $0$ and solve for $u$ .

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Step 3.8.1

Set $u - 144$ equal to $0$ .

$u - 144 = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.8.2

Add $144$ to both sides of the equation.

$u = 144$

$y = - 13 + \frac{x^{2}}{8}$

$u = 144$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.9

The final solution is all the values that make $u (u - 144) = 0$ true.

$u = 0, 144$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.10

Substitute the real value of $u = x^{2}$ back into the solved equation.

$x^{2} = 0$

$x^{2} = 144$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.11

Solve the first equation for $x$ .

$x^{2} = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.12

Solve the equation for $x$ .

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Step 3.12.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.12.2

Simplify $\pm \sqrt{0}$ .

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Step 3.12.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.12.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.12.2.3

Plus or minus $0$ is $0$ .

$x = 0$

$y = - 13 + \frac{x^{2}}{8}$

$x = 0$

$y = - 13 + \frac{x^{2}}{8}$

$x = 0$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.13

Solve the second equation for $x$ .

$x^{2} = 144$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.14

Solve the equation for $x$ .

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Step 3.14.1

Remove parentheses.

$x^{2} = 144$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.14.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{144}$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.14.3

Simplify $\pm \sqrt{144}$ .

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Step 3.14.3.1

Rewrite $144$ as $12^{2}$ .

$x = \pm \sqrt{12^{2}}$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.14.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 12$

$y = - 13 + \frac{x^{2}}{8}$

$x = \pm 12$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.14.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.14.4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 12$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.14.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 12$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.14.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 12, - 12$

$y = - 13 + \frac{x^{2}}{8}$

$x = 12, - 12$

$y = - 13 + \frac{x^{2}}{8}$

$x = 12, - 12$

$y = - 13 + \frac{x^{2}}{8}$

Step 3.15

The solution to $\frac{x^{4}}{64} - \frac{9 x^{2}}{4} + 169 = 169$ is $x = 0, 12, - 12$ .

$x = 0, 12, - 12$

$y = - 13 + \frac{x^{2}}{8}$

$x = 0, 12, - 12$

$y = - 13 + \frac{x^{2}}{8}$

Step 4

Replace all occurrences of $x$ with $0$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = - 13 + \frac{x^{2}}{8}$ with $0$ .

$y = - 13 + \frac{{(0)}^{2}}{8}$

$x = 0$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 13 + \frac{{(0)}^{2}}{8}$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

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

$y = - 13 + \frac{0}{8}$

$x = 0$

Step 4.2.1.1.2

Divide $0$ by $8$ .

$y = - 13 + 0$

$x = 0$

$y = - 13 + 0$

$x = 0$

Step 4.2.1.2

Add $- 13$ and $0$ .

$y = - 13$

$x = 0$

$y = - 13$

$x = 0$

$y = - 13$

$x = 0$

$y = - 13$

$x = 0$

Step 5

Replace all occurrences of $x$ with $12$ in each equation.

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Step 5.1

Replace all occurrences of $x$ in $y = - 13 + \frac{x^{2}}{8}$ with $12$ .

$y = - 13 + \frac{{(12)}^{2}}{8}$

$x = 12$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 13 + \frac{{(12)}^{2}}{8}$ .

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Step 5.2.1.1

Simplify each term.

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Step 5.2.1.1.1

Raise $12$ to the power of $2$ .

$y = - 13 + \frac{144}{8}$

$x = 12$

Step 5.2.1.1.2

Divide $144$ by $8$ .

$y = - 13 + 18$

$x = 12$

$y = - 13 + 18$

$x = 12$

Step 5.2.1.2

Add $- 13$ and $18$ .

$y = 5$

$x = 12$

$y = 5$

$x = 12$

$y = 5$

$x = 12$

$y = 5$

$x = 12$

Step 6

Replace all occurrences of $x$ with $0$ in each equation.

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Step 6.1

Replace all occurrences of $x$ in $y = - 13 + \frac{x^{2}}{8}$ with $0$ .

$y = - 13 + \frac{{(0)}^{2}}{8}$

$x = 0$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- 13 + \frac{{(0)}^{2}}{8}$ .

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Step 6.2.1.1

Simplify each term.

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Step 6.2.1.1.1

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

$y = - 13 + \frac{0}{8}$

$x = 0$

Step 6.2.1.1.2

Divide $0$ by $8$ .

$y = - 13 + 0$

$x = 0$

$y = - 13 + 0$

$x = 0$

Step 6.2.1.2

Add $- 13$ and $0$ .

$y = - 13$

$x = 0$

$y = - 13$

$x = 0$

$y = - 13$

$x = 0$

$y = - 13$

$x = 0$

Step 7

Replace all occurrences of $x$ with $12$ in each equation.

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Step 7.1

Replace all occurrences of $x$ in $y = - 13 + \frac{x^{2}}{8}$ with $12$ .

$y = - 13 + \frac{{(12)}^{2}}{8}$

$x = 12$

Step 7.2

Simplify the right side.

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Step 7.2.1

Simplify $- 13 + \frac{{(12)}^{2}}{8}$ .

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Step 7.2.1.1

Simplify each term.

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Step 7.2.1.1.1

Raise $12$ to the power of $2$ .

$y = - 13 + \frac{144}{8}$

$x = 12$

Step 7.2.1.1.2

Divide $144$ by $8$ .

$y = - 13 + 18$

$x = 12$

$y = - 13 + 18$

$x = 12$

Step 7.2.1.2

Add $- 13$ and $18$ .

$y = 5$

$x = 12$

$y = 5$

$x = 12$

$y = 5$

$x = 12$

$y = 5$

$x = 12$

Step 8

Replace all occurrences of $x$ with $- 12$ in each equation.

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Step 8.1

Replace all occurrences of $x$ in $y = - 13 + \frac{x^{2}}{8}$ with $- 12$ .

$y = - 13 + \frac{{(- 12)}^{2}}{8}$

$x = - 12$

Step 8.2

Simplify the right side.

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Step 8.2.1

Simplify $- 13 + \frac{{(- 12)}^{2}}{8}$ .

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Step 8.2.1.1

Simplify each term.

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Step 8.2.1.1.1

Raise $- 12$ to the power of $2$ .

$y = - 13 + \frac{144}{8}$

$x = - 12$

Step 8.2.1.1.2

Divide $144$ by $8$ .

$y = - 13 + 18$

$x = - 12$

$y = - 13 + 18$

$x = - 12$

Step 8.2.1.2

Add $- 13$ and $18$ .

$y = 5$

$x = - 12$

$y = 5$

$x = - 12$

$y = 5$

$x = - 12$

$y = 5$

$x = - 12$

Step 9

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

$(0, - 13)$

$(12, 5)$

$(- 12, 5)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(0, - 13), (12, 5), (- 12, 5)$

Equation Form:

$x = 0, y = - 13$

$x = 12, y = 5$

$x = - 12, y = 5$

Step 11