Finite Math Examples

$y = - 42 x - 4$ , $y = 2 x^{2} - 42 x - 36$

Step 1

Eliminate the equal sides of each equation and combine.

$- 42 x - 4 = 2 x^{2} - 42 x - 36$

Step 2

Solve $- 42 x - 4 = 2 x^{2} - 42 x - 36$ for $x$ .

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Step 2.1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 x^{2} - 42 x - 36 = - 42 x - 4$

Step 2.2

Move all terms containing $x$ to the left side of the equation.

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Step 2.2.1

Add $42 x$ to both sides of the equation.

$2 x^{2} - 42 x - 36 + 42 x = - 4$

Step 2.2.2

Combine the opposite terms in $2 x^{2} - 42 x - 36 + 42 x$ .

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Step 2.2.2.1

Add $- 42 x$ and $42 x$ .

$2 x^{2} + 0 - 36 = - 4$

Step 2.2.2.2

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

$2 x^{2} - 36 = - 4$

Step 2.3

Move all terms not containing $x$ to the right side of the equation.

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Step 2.3.1

Add $36$ to both sides of the equation.

$2 x^{2} = - 4 + 36$

Step 2.3.2

Add $- 4$ and $36$ .

$2 x^{2} = 32$

Step 2.4

Divide each term in $2 x^{2} = 32$ by $2$ and simplify.

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Step 2.4.1

Divide each term in $2 x^{2} = 32$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{32}{2}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $2$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{32}{2}$

Step 2.4.2.1.2

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

$x^{2} = \frac{32}{2}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $32$ by $2$ .

$x^{2} = 16$

Step 2.5

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

$x = \pm \sqrt{16}$

Step 2.6

Simplify $\pm \sqrt{16}$ .

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Step 2.6.1

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

Step 2.6.2

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

$x = \pm 4$

Step 2.7

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

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Step 2.7.1

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

$x = 4$

Step 2.7.2

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

$x = - 4$

Step 2.7.3

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

$x = 4, - 4$

Step 3

Evaluate $y$ when $x = 4$ .

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Step 3.1

Substitute $4$ for $x$ .

$y = 2 {(4)}^{2} - 42 \cdot 4 - 36$

Step 3.2

Substitute $4$ for $x$ in $y = 2 {(4)}^{2} - 42 \cdot 4 - 36$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = 2 \cdot 4^{2} - 42 \cdot 4 - 36$

Step 3.2.2

Remove parentheses.

$y = 2 {(4)}^{2} - 42 \cdot 4 - 36$

Step 3.2.3

Simplify $2 {(4)}^{2} - 42 \cdot 4 - 36$ .

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Raise $4$ to the power of $2$ .

$y = 2 \cdot 16 - 42 \cdot 4 - 36$

Step 3.2.3.1.2

Multiply $2$ by $16$ .

$y = 32 - 42 \cdot 4 - 36$

Step 3.2.3.1.3

Multiply $- 42$ by $4$ .

$y = 32 - 168 - 36$

Step 3.2.3.2

Simplify by subtracting numbers.

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Step 3.2.3.2.1

Subtract $168$ from $32$ .

$y = - 136 - 36$

Step 3.2.3.2.2

Subtract $36$ from $- 136$ .

$y = - 172$

Step 4

Evaluate $y$ when $x = - 4$ .

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Step 4.1

Substitute $- 4$ for $x$ .

$y = 2 {(- 4)}^{2} - 42 \cdot - 4 - 36$

Step 4.2

Substitute $- 4$ for $x$ in $y = 2 {(- 4)}^{2} - 42 \cdot - 4 - 36$ and solve for $y$ .

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Step 4.2.1

Remove parentheses.

$y = 2 {(- 4)}^{2} - 42 \cdot - 4 - 36$

Step 4.2.2

Simplify $2 {(- 4)}^{2} - 42 \cdot - 4 - 36$ .

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Step 4.2.2.1

Simplify each term.

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Step 4.2.2.1.1

Raise $- 4$ to the power of $2$ .

$y = 2 \cdot 16 - 42 \cdot - 4 - 36$

Step 4.2.2.1.2

Multiply $2$ by $16$ .

$y = 32 - 42 \cdot - 4 - 36$

Step 4.2.2.1.3

Multiply $- 42$ by $- 4$ .

$y = 32 + 168 - 36$

Step 4.2.2.2

Simplify by adding and subtracting.

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Step 4.2.2.2.1

Add $32$ and $168$ .

$y = 200 - 36$

Step 4.2.2.2.2

Subtract $36$ from $200$ .

$y = 164$

Step 5

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

$(4, - 172)$

$(- 4, 164)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 172), (- 4, 164)$

Equation Form:

$x = 4, y = - 172$

$x = - 4, y = 164$

Step 7