Finite Math Examples

$x = - 2 (x + 2) (x - 1) (x - 4)$

Step 1

Simplify $- 2 (x + 2) (x - 1) (x - 4)$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

$x = (- 2 x - 2 \cdot 2) (x - 1) (x - 4)$

Step 1.1.2

Multiply $- 2$ by $2$ .

$x = (- 2 x - 4) (x - 1) (x - 4)$

Step 1.2

Expand $(- 2 x - 4) (x - 1)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x = (- 2 x (x - 1) - 4 (x - 1)) (x - 4)$

Step 1.2.2

Apply the distributive property.

$x = (- 2 x \cdot x - 2 x \cdot - 1 - 4 (x - 1)) (x - 4)$

Step 1.2.3

Apply the distributive property.

$x = (- 2 x \cdot x - 2 x \cdot - 1 - 4 x - 4 \cdot - 1) (x - 4)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1.1.1

Move $x$ .

$x = (- 2 (x \cdot x) - 2 x \cdot - 1 - 4 x - 4 \cdot - 1) (x - 4)$

Step 1.3.1.1.2

Multiply $x$ by $x$ .

$x = (- 2 x^{2} - 2 x \cdot - 1 - 4 x - 4 \cdot - 1) (x - 4)$

Step 1.3.1.2

Multiply $- 1$ by $- 2$ .

$x = (- 2 x^{2} + 2 x - 4 x - 4 \cdot - 1) (x - 4)$

Step 1.3.1.3

Multiply $- 4$ by $- 1$ .

$x = (- 2 x^{2} + 2 x - 4 x + 4) (x - 4)$

Step 1.3.2

Subtract $4 x$ from $2 x$ .

$x = (- 2 x^{2} - 2 x + 4) (x - 4)$

Step 1.4

Expand $(- 2 x^{2} - 2 x + 4) (x - 4)$ by multiplying each term in the first expression by each term in the second expression.

$x = - 2 x^{2} x - 2 x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5

Simplify terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

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

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Step 1.5.1.1.1

Move $x$ .

$x = - 2 (x \cdot x^{2}) - 2 x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5.1.1.2

Multiply $x$ by $x^{2}$ .

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Step 1.5.1.1.2.1

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

$x = - 2 (x^{1} x^{2}) - 2 x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5.1.1.2.2

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

$x = - 2 x^{1 + 2} - 2 x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5.1.1.3

Add $1$ and $2$ .

$x = - 2 x^{3} - 2 x^{2} \cdot - 4 - 2 x \cdot x - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5.1.2

Multiply $- 4$ by $- 2$ .

$x = - 2 x^{3} + 8 x^{2} - 2 x \cdot x - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 1.5.1.3.1

Move $x$ .

$x = - 2 x^{3} + 8 x^{2} - 2 (x \cdot x) - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5.1.3.2

Multiply $x$ by $x$ .

$x = - 2 x^{3} + 8 x^{2} - 2 x^{2} - 2 x \cdot - 4 + 4 x + 4 \cdot - 4$

Step 1.5.1.4

Multiply $- 4$ by $- 2$ .

$x = - 2 x^{3} + 8 x^{2} - 2 x^{2} + 8 x + 4 x + 4 \cdot - 4$

Step 1.5.1.5

Multiply $4$ by $- 4$ .

$x = - 2 x^{3} + 8 x^{2} - 2 x^{2} + 8 x + 4 x - 16$

Step 1.5.2

Simplify by adding terms.

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Step 1.5.2.1

Subtract $2 x^{2}$ from $8 x^{2}$ .

$x = - 2 x^{3} + 6 x^{2} + 8 x + 4 x - 16$

Step 1.5.2.2

Add $8 x$ and $4 x$ .

$x = - 2 x^{3} + 6 x^{2} + 12 x - 16$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 1.94445423, 1.0588475, 3.88560673$

Step 3

The domain is the set of all valid $x$ values.

$> (S E T, x | x \approx - 1.94445423, 1.0588475, 3.88560673)$

Step 4