Basic Math Examples

$0 = 0 + 15 t + 0.5 \cdot (- 9.81) \cdot t^{2}$

Step 1

Rewrite the equation as $0 + 15 t + 0.5 \cdot (- 9.81) \cdot t^{2} = 0$ .

$0 + 15 t + 0.5 \cdot (- 9.81) \cdot t^{2} = 0$

Step 2

Simplify $0 + 15 t + 0.5 \cdot (- 9.81) \cdot t^{2}$ .

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Step 2.1

Add $0$ and $15 t$ .

$15 t + 0.5 \cdot (- 9.81) \cdot t^{2} = 0$

Step 2.2

Multiply $0.5$ by $- 9.81$ .

$15 t - 4.905 t^{2} = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

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

$15 u - 4.905 u^{2} = 0$

Step 3.2

Factor $0.015 u$ out of $15 u - 4.905 u^{2}$ .

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Step 3.2.1

Factor $0.015 u$ out of $15 u$ .

$0.015 u (1000) - 4.905 u^{2} = 0$

Step 3.2.2

Factor $0.015 u$ out of $- 4.905 u^{2}$ .

$0.015 u (1000) + 0.015 u (- 327 u) = 0$

Step 3.2.3

Factor $0.015 u$ out of $0.015 u (1000) + 0.015 u (- 327 u)$ .

$0.015 u (1000 - 327 u) = 0$

Step 3.3

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

$0.015 t (1000 - 327 t) = 0$

Step 4

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

$t = 0$

$1000 - 327 t = 0$

Step 5

Set $t$ equal to $0$ .

$t = 0$

Step 6

Set $1000 - 327 t$ equal to $0$ and solve for $t$ .

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Step 6.1

Set $1000 - 327 t$ equal to $0$ .

$1000 - 327 t = 0$

Step 6.2

Solve $1000 - 327 t = 0$ for $t$ .

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Step 6.2.1

Subtract $1000$ from both sides of the equation.

$- 327 t = - 1000$

Step 6.2.2

Divide each term in $- 327 t = - 1000$ by $- 327$ and simplify.

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Step 6.2.2.1

Divide each term in $- 327 t = - 1000$ by $- 327$ .

$\frac{- 327 t}{- 327} = \frac{- 1000}{- 327}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $- 327$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{- 327 t}{- 327} = \frac{- 1000}{- 327}$

Step 6.2.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 1000}{- 327}$

Step 6.2.2.3

Simplify the right side.

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Step 6.2.2.3.1

Dividing two negative values results in a positive value.

$t = \frac{1000}{327}$

Step 7

The final solution is all the values that make $0.015 t (1000 - 327 t) = 0$ true.

$t = 0, \frac{1000}{327}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$t = 0, \frac{1000}{327}$

Decimal Form:

$t = 0, 3.05810397 \dots$

Mixed Number Form:

$t = 0, 3 \frac{19}{327}$