Finite Math Examples

$p (x) = 120 x - x^{2}$

Step 1

Set $120 x - x^{2}$ equal to $0$ .

$120 x - x^{2} = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Factor the left side of the equation.

Tap for more steps...

Step 2.1.1

Let $u = x$ . Substitute $u$ for all occurrences of $x$ .

$120 u - u^{2} = 0$

Step 2.1.2

Factor $u$ out of $120 u - u^{2}$ .

Tap for more steps...

Step 2.1.2.1

Factor $u$ out of $120 u$ .

$u \cdot 120 - u^{2} = 0$

Step 2.1.2.2

Factor $u$ out of $- u^{2}$ .

$u \cdot 120 + u (- u) = 0$

Step 2.1.2.3

Factor $u$ out of $u \cdot 120 + u (- u)$ .

$u (120 - u) = 0$

Step 2.1.3

Replace all occurrences of $u$ with $x$ .

$x (120 - x) = 0$

Step 2.2

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

$x = 0$

$120 - x = 0$

Step 2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.4

Set $120 - x$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.4.1

Set $120 - x$ equal to $0$ .

$120 - x = 0$

Step 2.4.2

Solve $120 - x = 0$ for $x$ .

Tap for more steps...

Step 2.4.2.1

Subtract $120$ from both sides of the equation.

$- x = - 120$

Step 2.4.2.2

Divide each term in $- x = - 120$ by $- 1$ and simplify.

Tap for more steps...

Step 2.4.2.2.1

Divide each term in $- x = - 120$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 120}{- 1}$

Step 2.4.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 120}{- 1}$

Step 2.4.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 120}{- 1}$

Step 2.4.2.2.3

Simplify the right side.

Tap for more steps...

Step 2.4.2.2.3.1

Divide $- 120$ by $- 1$ .

$x = 120$

Step 2.5

The final solution is all the values that make $x (120 - x) = 0$ true.

$x = 0, 120$

Step 3