Precalculus Examples

$y = (14 - x) (600 + 100 x)$

Step 1

Subtract $(14 - x) (600 + 100 x)$ from both sides of the equation.

$y - (14 - x) (600 + 100 x) = 0$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$y + (- 1 \cdot 14 - - x) (600 + 100 x) = 0$

Step 2.2

Multiply $- 1$ by $14$ .

$y + (- 14 - - x) (600 + 100 x) = 0$

Step 2.3

Multiply $- - x$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$y + (- 14 + 1 x) (600 + 100 x) = 0$

Step 2.3.2

Multiply $x$ by $1$ .

$y + (- 14 + x) (600 + 100 x) = 0$

Step 2.4

Expand $(- 14 + x) (600 + 100 x)$ using the FOIL Method.

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Step 2.4.1

Apply the distributive property.

$y - 14 (600 + 100 x) + x (600 + 100 x) = 0$

Step 2.4.2

Apply the distributive property.

$y - 14 \cdot 600 - 14 (100 x) + x (600 + 100 x) = 0$

Step 2.4.3

Apply the distributive property.

$y - 14 \cdot 600 - 14 (100 x) + x \cdot 600 + x (100 x) = 0$

Step 2.5

Simplify and combine like terms.

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Step 2.5.1

Simplify each term.

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Step 2.5.1.1

Multiply $- 14$ by $600$ .

$y - 8400 - 14 (100 x) + x \cdot 600 + x (100 x) = 0$

Step 2.5.1.2

Multiply $100$ by $- 14$ .

$y - 8400 - 1400 x + x \cdot 600 + x (100 x) = 0$

Step 2.5.1.3

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

$y - 8400 - 1400 x + 600 \cdot x + x (100 x) = 0$

Step 2.5.1.4

Rewrite using the commutative property of multiplication.

$y - 8400 - 1400 x + 600 x + 100 x \cdot x = 0$

Step 2.5.1.5

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

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Step 2.5.1.5.1

Move $x$ .

$y - 8400 - 1400 x + 600 x + 100 (x \cdot x) = 0$

Step 2.5.1.5.2

Multiply $x$ by $x$ .

$y - 8400 - 1400 x + 600 x + 100 x^{2} = 0$

Step 2.5.2

Add $- 1400 x$ and $600 x$ .

$y - 8400 - 800 x + 100 x^{2} = 0$

Step 3

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

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Step 3.1

Add $8400$ to both sides of the equation.

$y - 800 x + 100 x^{2} = 8400$

Step 3.2

Add $800 x$ to both sides of the equation.

$y + 100 x^{2} = 8400 + 800 x$

Step 3.3

Subtract $100 x^{2}$ from both sides of the equation.

$y = 8400 + 800 x - 100 x^{2}$