Trigonometry Examples

$70 = 70 - 10 t - 5 t^{2}$

Step 1

Rewrite the equation as $70 - 10 t - 5 t^{2} = 70$ .

$70 - 10 t - 5 t^{2} = 70$

Step 2

Subtract $70$ from both sides of the equation.

$70 - 10 t - 5 t^{2} - 70 = 0$

Step 3

Combine the opposite terms in $70 - 10 t - 5 t^{2} - 70$ .

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Step 3.1

Subtract $70$ from $70$ .

$- 10 t - 5 t^{2} + 0 = 0$

Step 3.2

Add $- 10 t - 5 t^{2}$ and $0$ .

$- 10 t - 5 t^{2} = 0$

Step 4

Factor $- 5 t$ out of $- 10 t - 5 t^{2}$ .

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Step 4.1

Reorder $- 10 t$ and $- 5 t^{2}$ .

$- 5 t^{2} - 10 t = 0$

Step 4.2

Factor $- 5 t$ out of $- 5 t^{2}$ .

$- 5 t \cdot t - 10 t = 0$

Step 4.3

Factor $- 5 t$ out of $- 10 t$ .

$- 5 t \cdot t - 5 t \cdot 2 = 0$

Step 4.4

Factor $- 5 t$ out of $- 5 t (t) - 5 t (2)$ .

$- 5 t (t + 2) = 0$

Step 5

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

$t = 0$

$t + 2 = 0$

Step 6

Set $t$ equal to $0$ .

$t = 0$

Step 7

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

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Step 7.1

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

$t + 2 = 0$

Step 7.2

Subtract $2$ from both sides of the equation.

$t = - 2$

Step 8

The final solution is all the values that make $- 5 t (t + 2) = 0$ true.

$t = 0, - 2$