Trigonometry Examples

$140 = 140 - 8 t - 16 t^{2}$

Step 1

Rewrite the equation as $140 - 8 t - 16 t^{2} = 140$ .

$140 - 8 t - 16 t^{2} = 140$

Step 2

Subtract $140$ from both sides of the equation.

$140 - 8 t - 16 t^{2} - 140 = 0$

Step 3

Combine the opposite terms in $140 - 8 t - 16 t^{2} - 140$ .

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Step 3.1

Subtract $140$ from $140$ .

$- 8 t - 16 t^{2} + 0 = 0$

Step 3.2

Add $- 8 t - 16 t^{2}$ and $0$ .

$- 8 t - 16 t^{2} = 0$

Step 4

Factor $- 8 t$ out of $- 8 t - 16 t^{2}$ .

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Step 4.1

Reorder $- 8 t$ and $- 16 t^{2}$ .

$- 16 t^{2} - 8 t = 0$

Step 4.2

Factor $- 8 t$ out of $- 16 t^{2}$ .

$- 8 t (2 t) - 8 t = 0$

Step 4.3

Factor $- 8 t$ out of $- 8 t$ .

$- 8 t (2 t) - 8 t \cdot 1 = 0$

Step 4.4

Factor $- 8 t$ out of $- 8 t (2 t) - 8 t (1)$ .

$- 8 t (2 t + 1) = 0$

Step 5

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

$t = 0$

$2 t + 1 = 0$

Step 6

Set $t$ equal to $0$ .

$t = 0$

Step 7

Set $2 t + 1$ equal to $0$ and solve for $t$ .

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Step 7.1

Set $2 t + 1$ equal to $0$ .

$2 t + 1 = 0$

Step 7.2

Solve $2 t + 1 = 0$ for $t$ .

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Step 7.2.1

Subtract $1$ from both sides of the equation.

$2 t = - 1$

Step 7.2.2

Divide each term in $2 t = - 1$ by $2$ and simplify.

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Step 7.2.2.1

Divide each term in $2 t = - 1$ by $2$ .

$\frac{2 t}{2} = \frac{- 1}{2}$

Step 7.2.2.2

Simplify the left side.

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Step 7.2.2.2.1

Cancel the common factor of $2$ .

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Step 7.2.2.2.1.1

Cancel the common factor.

$\frac{2 t}{2} = \frac{- 1}{2}$

Step 7.2.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{- 1}{2}$

Step 7.2.2.3

Simplify the right side.

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Step 7.2.2.3.1

Move the negative in front of the fraction.

$t = - \frac{1}{2}$

Step 8

The final solution is all the values that make $- 8 t (2 t + 1) = 0$ true.

$t = 0, - \frac{1}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$t = 0, - \frac{1}{2}$

Decimal Form:

$t = 0, - 0.5$