Finite Math Examples

$f (x) = 72 x - 4 x^{2}$

Step 1

Set $72 x - 4 x^{2}$ equal to $0$ .

$72 x - 4 x^{2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor the left side of the equation.

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Step 2.1.1

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

$72 u - 4 u^{2} = 0$

Step 2.1.2

Factor $4 u$ out of $72 u - 4 u^{2}$ .

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Step 2.1.2.1

Factor $4 u$ out of $72 u$ .

$4 u (18) - 4 u^{2} = 0$

Step 2.1.2.2

Factor $4 u$ out of $- 4 u^{2}$ .

$4 u (18) + 4 u (- u) = 0$

Step 2.1.2.3

Factor $4 u$ out of $4 u (18) + 4 u (- u)$ .

$4 u (18 - u) = 0$

Step 2.1.3

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

$4 x (18 - x) = 0$

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 $0$ .

$x = 0$

$18 - x = 0$

Step 2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.4

Set $18 - x$ equal to $0$ and solve for $x$ .

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Step 2.4.1

Set $18 - x$ equal to $0$ .

$18 - x = 0$

Step 2.4.2

Solve $18 - x = 0$ for $x$ .

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Step 2.4.2.1

Subtract $18$ from both sides of the equation.

$- x = - 18$

Step 2.4.2.2

Divide each term in $- x = - 18$ by $- 1$ and simplify.

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Step 2.4.2.2.1

Divide each term in $- x = - 18$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 18}{- 1}$

Step 2.4.2.2.2

Simplify the left side.

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Step 2.4.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 18}{- 1}$

Step 2.4.2.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 18}{- 1}$

Step 2.4.2.2.3

Simplify the right side.

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Step 2.4.2.2.3.1

Divide $- 18$ by $- 1$ .

$x = 18$

Step 2.5

The final solution is all the values that make $4 x (18 - x) = 0$ true.

$x = 0, 18$

Step 3