Calculus Examples

$s (t) = 28 t - 0.8 t^{2}$

Step 1

Set $28 t - 0.8 t^{2}$ equal to $0$ .

$28 t - 0.8 t^{2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Factor $0.8 t$ out of $28 t - 0.8 t^{2}$ .

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Step 2.1.1

Factor $0.8 t$ out of $28 t$ .

$0.8 t (35) - 0.8 t^{2} = 0$

Step 2.1.2

Factor $0.8 t$ out of $- 0.8 t^{2}$ .

$0.8 t (35) + 0.8 t (- t) = 0$

Step 2.1.3

Factor $0.8 t$ out of $0.8 t (35) + 0.8 t (- t)$ .

$0.8 t (35 - t) = 0$

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 $0$ .

$t = 0$

$35 - t = 0$

Step 2.3

Set $t$ equal to $0$ .

$t = 0$

Step 2.4

Set $35 - t$ equal to $0$ and solve for $t$ .

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Step 2.4.1

Set $35 - t$ equal to $0$ .

$35 - t = 0$

Step 2.4.2

Solve $35 - t = 0$ for $t$ .

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Step 2.4.2.1

Subtract $35$ from both sides of the equation.

$- t = - 35$

Step 2.4.2.2

Divide each term in $- t = - 35$ by $- 1$ and simplify.

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Step 2.4.2.2.1

Divide each term in $- t = - 35$ by $- 1$ .

$\frac{- t}{- 1} = \frac{- 35}{- 1}$

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.

$\frac{t}{1} = \frac{- 35}{- 1}$

Step 2.4.2.2.2.2

Divide $t$ by $1$ .

$t = \frac{- 35}{- 1}$

Step 2.4.2.2.3

Simplify the right side.

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Step 2.4.2.2.3.1

Divide $- 35$ by $- 1$ .

$t = 35$

Step 2.5

The final solution is all the values that make $0.8 t (35 - t) = 0$ true.

$t = 0, 35$

Step 3