Calculus Examples

$x (30) = 9 x - 0.01 x^{2}$

Step 1

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

$9 x - 0.01 x^{2} = x (30)$

Step 2

Move $30$ to the left of $x$ .

$9 x - 0.01 x^{2} = 30 x$

Step 3

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

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Step 3.1

Subtract $30 x$ from both sides of the equation.

$9 x - 0.01 x^{2} - 30 x = 0$

Step 3.2

Subtract $30 x$ from $9 x$ .

$- 0.01 x^{2} - 21 x = 0$

Step 4

Factor $- 0.01 x$ out of $- 0.01 x^{2} - 21 x$ .

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Step 4.1

Factor $- 0.01 x$ out of $- 0.01 x^{2}$ .

$- 0.01 x \cdot x - 21 x = 0$

Step 4.2

Factor $- 0.01 x$ out of $- 21 x$ .

$- 0.01 x \cdot x - 0.01 x \cdot 2100 = 0$

Step 4.3

Factor $- 0.01 x$ out of $- 0.01 x (x) - 0.01 x (2100)$ .

$- 0.01 x (x + 2100) = 0$

Step 5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 2100 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

Set $x + 2100$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 2100$ equal to $0$ .

$x + 2100 = 0$

Step 7.2

Subtract $2100$ from both sides of the equation.

$x = - 2100$

Step 8

The final solution is all the values that make $- 0.01 x (x + 2100) = 0$ true.

$x = 0, - 2100$