Finite Math Examples

$1296 x^{2} + 36 (x^{2} - 36) y^{2} = 46656$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$1296 x^{2} + 36 (x^{2} - 36) {(0)}^{2} = 46656$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $1296 x^{2} + 36 (x^{2} - 36) {(0)}^{2}$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$1296 x^{2} + (36 x^{2} + 36 \cdot - 36) {(0)}^{2} = 46656$

Step 1.2.1.1.2

Multiply $36$ by $- 36$ .

$1296 x^{2} + (36 x^{2} - 1296) {(0)}^{2} = 46656$

Step 1.2.1.1.3

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

$1296 x^{2} + (36 x^{2} - 1296) \cdot 0 = 46656$

Step 1.2.1.1.4

Multiply $36 x^{2} - 1296$ by $0$ .

$1296 x^{2} + 0 = 46656$

Step 1.2.1.2

Add $1296 x^{2}$ and $0$ .

$1296 x^{2} = 46656$

Step 1.2.2

Divide each term in $1296 x^{2} = 46656$ by $1296$ and simplify.

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Step 1.2.2.1

Divide each term in $1296 x^{2} = 46656$ by $1296$ .

$\frac{1296 x^{2}}{1296} = \frac{46656}{1296}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $1296$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{1296 x^{2}}{1296} = \frac{46656}{1296}$

Step 1.2.2.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{46656}{1296}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide $46656$ by $1296$ .

$x^{2} = 36$

Step 1.2.3

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

$x = \pm \sqrt{36}$

Step 1.2.4

Simplify $\pm \sqrt{36}$ .

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Step 1.2.4.1

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

Step 1.2.4.2

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

$x = \pm 6$

Step 1.2.5

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

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Step 1.2.5.1

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

$x = 6$

Step 1.2.5.2

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

$x = - 6$

Step 1.2.5.3

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

$x = 6, - 6$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(6, 0), (- 6, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$1296 {(0)}^{2} + 36 ({(0)}^{2} - 36) \cdot y^{2} = 46656$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $1296 {(0)}^{2} + 36 ({(0)}^{2} - 36) \cdot y^{2}$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

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

$1296 \cdot 0 + 36 ({(0)}^{2} - 36) \cdot y^{2} = 46656$

Step 2.2.1.1.2

Multiply $1296$ by $0$ .

$0 + 36 ({(0)}^{2} - 36) \cdot y^{2} = 46656$

Step 2.2.1.1.3

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

$0 + 36 (0 - 36) \cdot y^{2} = 46656$

Step 2.2.1.1.4

Subtract $36$ from $0$ .

$0 + 36 \cdot - 36 \cdot y^{2} = 46656$

Step 2.2.1.1.5

Multiply $36$ by $- 36$ .

$0 - 1296 y^{2} = 46656$

Step 2.2.1.2

Subtract $1296 y^{2}$ from $0$ .

$- 1296 y^{2} = 46656$

Step 2.2.2

Divide each term in $- 1296 y^{2} = 46656$ by $- 1296$ and simplify.

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Step 2.2.2.1

Divide each term in $- 1296 y^{2} = 46656$ by $- 1296$ .

$\frac{- 1296 y^{2}}{- 1296} = \frac{46656}{- 1296}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $- 1296$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{- 1296 y^{2}}{- 1296} = \frac{46656}{- 1296}$

Step 2.2.2.2.1.2

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{46656}{- 1296}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide $46656$ by $- 1296$ .

$y^{2} = - 36$

Step 2.2.3

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

$y = \pm \sqrt{- 36}$

Step 2.2.4

Simplify $\pm \sqrt{- 36}$ .

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Step 2.2.4.1

Rewrite $- 36$ as $- 1 (36)$ .

$y = \pm \sqrt{- 1 (36)}$

Step 2.2.4.2

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$y = \pm \sqrt{- 1} \cdot \sqrt{36}$

Step 2.2.4.3

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \pm i \cdot \sqrt{36}$

Step 2.2.4.4

Rewrite $36$ as $6^{2}$ .

$y = \pm i \cdot \sqrt{6^{2}}$

Step 2.2.4.5

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

$y = \pm i \cdot 6$

Step 2.2.4.6

Move $6$ to the left of $i$ .

$y = \pm 6 i$

Step 2.2.5

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

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Step 2.2.5.1

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

$y = 6 i$

Step 2.2.5.2

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

$y = - 6 i$

Step 2.2.5.3

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

$y = 6 i, - 6 i$

Step 2.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(6, 0), (- 6, 0)$

y-intercept(s): $None$

Step 4