Finite Math Examples

$x (x + 10) (40 - 2 x) = 1998$

Step 1

Simplify $x (x + 10) (40 - 2 x)$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

$(x \cdot x + x \cdot 10) (40 - 2 x) = 1998$

Step 1.1.2

Simplify the expression.

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Step 1.1.2.1

Multiply $x$ by $x$ .

$(x^{2} + x \cdot 10) (40 - 2 x) = 1998$

Step 1.1.2.2

Move $10$ to the left of $x$ .

$(x^{2} + 10 \cdot x) (40 - 2 x) = 1998$

Step 1.2

Expand $(x^{2} + 10 x) (40 - 2 x)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x^{2} (40 - 2 x) + 10 x (40 - 2 x) = 1998$

Step 1.2.2

Apply the distributive property.

$x^{2} \cdot 40 + x^{2} (- 2 x) + 10 x (40 - 2 x) = 1998$

Step 1.2.3

Apply the distributive property.

$x^{2} \cdot 40 + x^{2} (- 2 x) + 10 x \cdot 40 + 10 x (- 2 x) = 1998$

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

Move $40$ to the left of $x^{2}$ .

$40 \cdot x^{2} + x^{2} (- 2 x) + 10 x \cdot 40 + 10 x (- 2 x) = 1998$

Step 1.3.1.2

Rewrite using the commutative property of multiplication.

$40 x^{2} - 2 x^{2} x + 10 x \cdot 40 + 10 x (- 2 x) = 1998$

Step 1.3.1.3

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

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Step 1.3.1.3.1

Move $x$ .

$40 x^{2} - 2 (x \cdot x^{2}) + 10 x \cdot 40 + 10 x (- 2 x) = 1998$

Step 1.3.1.3.2

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

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Step 1.3.1.3.2.1

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

$40 x^{2} - 2 (x^{1} x^{2}) + 10 x \cdot 40 + 10 x (- 2 x) = 1998$

Step 1.3.1.3.2.2

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

$40 x^{2} - 2 x^{1 + 2} + 10 x \cdot 40 + 10 x (- 2 x) = 1998$

Step 1.3.1.3.3

Add $1$ and $2$ .

$40 x^{2} - 2 x^{3} + 10 x \cdot 40 + 10 x (- 2 x) = 1998$

Step 1.3.1.4

Multiply $40$ by $10$ .

$40 x^{2} - 2 x^{3} + 400 x + 10 x (- 2 x) = 1998$

Step 1.3.1.5

Rewrite using the commutative property of multiplication.

$40 x^{2} - 2 x^{3} + 400 x + 10 \cdot - 2 x \cdot x = 1998$

Step 1.3.1.6

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

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Step 1.3.1.6.1

Move $x$ .

$40 x^{2} - 2 x^{3} + 400 x + 10 \cdot - 2 (x \cdot x) = 1998$

Step 1.3.1.6.2

Multiply $x$ by $x$ .

$40 x^{2} - 2 x^{3} + 400 x + 10 \cdot - 2 x^{2} = 1998$

Step 1.3.1.7

Multiply $10$ by $- 2$ .

$40 x^{2} - 2 x^{3} + 400 x - 20 x^{2} = 1998$

Step 1.3.2

Subtract $20 x^{2}$ from $40 x^{2}$ .

$20 x^{2} - 2 x^{3} + 400 x = 1998$

Step 2

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

$x \approx - 12.46785726, 4.44606335, 18.0217939$

Step 3