Finite Math Examples

$(5 (600 + x) - 0.005 {(600 + x)}^{2}) - (5 (600) - 0.005 {(600)}^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 \cdot 600 + 5 x - 0.005 {(600 + x)}^{2} - (5 (600) - 0.005 {(600)}^{2})$

Step 1.2

Multiply $5$ by $600$ .

$3000 + 5 x - 0.005 {(600 + x)}^{2} - (5 (600) - 0.005 {(600)}^{2})$

Step 1.3

Rewrite ${(600 + x)}^{2}$ as $(600 + x) (600 + x)$ .

$3000 + 5 x - 0.005 ((600 + x) (600 + x)) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.4

Expand $(600 + x) (600 + x)$ using the FOIL Method.

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Step 1.4.1

Apply the distributive property.

$3000 + 5 x - 0.005 (600 (600 + x) + x (600 + x)) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.4.2

Apply the distributive property.

$3000 + 5 x - 0.005 (600 \cdot 600 + 600 x + x (600 + x)) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.4.3

Apply the distributive property.

$3000 + 5 x - 0.005 (600 \cdot 600 + 600 x + x \cdot 600 + x \cdot x) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.5

Simplify and combine like terms.

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Step 1.5.1

Simplify each term.

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Step 1.5.1.1

Multiply $600$ by $600$ .

$3000 + 5 x - 0.005 (360000 + 600 x + x \cdot 600 + x \cdot x) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.5.1.2

Move $600$ to the left of $x$ .

$3000 + 5 x - 0.005 (360000 + 600 x + 600 \cdot x + x \cdot x) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.5.1.3

Multiply $x$ by $x$ .

$3000 + 5 x - 0.005 (360000 + 600 x + 600 x + x^{2}) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.5.2

Add $600 x$ and $600 x$ .

$3000 + 5 x - 0.005 (360000 + 1200 x + x^{2}) - (5 (600) - 0.005 {(600)}^{2})$

Step 1.6

Apply the distributive property.

$3000 + 5 x - 0.005 \cdot 360000 - 0.005 (1200 x) - 0.005 x^{2} - (5 (600) - 0.005 {(600)}^{2})$

Step 1.7

Simplify.

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Step 1.7.1

Multiply $- 0.005$ by $360000$ .

$3000 + 5 x - 1800 - 0.005 (1200 x) - 0.005 x^{2} - (5 (600) - 0.005 {(600)}^{2})$

Step 1.7.2

Multiply $1200$ by $- 0.005$ .

$3000 + 5 x - 1800 - 6 x - 0.005 x^{2} - (5 (600) - 0.005 {(600)}^{2})$

Step 1.8

Simplify each term.

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Step 1.8.1

Multiply $5$ by $600$ .

$3000 + 5 x - 1800 - 6 x - 0.005 x^{2} - (3000 - 0.005 {(600)}^{2})$

Step 1.8.2

Raise $600$ to the power of $2$ .

$3000 + 5 x - 1800 - 6 x - 0.005 x^{2} - (3000 - 0.005 \cdot 360000)$

Step 1.8.3

Multiply $- 0.005$ by $360000$ .

$3000 + 5 x - 1800 - 6 x - 0.005 x^{2} - (3000 - 1800)$

Step 1.9

Subtract $1800$ from $3000$ .

$3000 + 5 x - 1800 - 6 x - 0.005 x^{2} - 1 \cdot 1200$

Step 1.10

Multiply $- 1$ by $1200$ .

$3000 + 5 x - 1800 - 6 x - 0.005 x^{2} - 1200$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $1800$ from $3000$ .

$5 x + 1200 - 6 x - 0.005 x^{2} - 1200$

Step 2.2

Combine the opposite terms in $5 x + 1200 - 6 x - 0.005 x^{2} - 1200$ .

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Step 2.2.1

Subtract $1200$ from $1200$ .

$5 x - 6 x - 0.005 x^{2} + 0$

Step 2.2.2

Add $5 x - 6 x - 0.005 x^{2}$ and $0$ .

$5 x - 6 x - 0.005 x^{2}$

Step 2.3

Subtract $6 x$ from $5 x$ .

$- 1 x - 0.005 x^{2}$