The pilot of a helicopter plans to release a bucket of water on a forest fire. The height y in feet of the water t seconds after its release is modeled by $y = -16t^2 - 2t + 400$. The horizontal distance $x$ in feet between the water and its point of release is modeled by $x = 91t$. To the nearest foot, at what horizontal distance from the target should the pilot begin releasing the water?
Okay, so I used the formula and got: $x = 2 \pm \frac{\sqrt{25604}}{800}$, but am not sure what to do after that.
First you have to find the time it takes for the water to hit the ground, which means solving this equation:
$$y=−16t^2−2t+400$$ Solving this (by setting $y=0$) you end up with the following for $t$ using the quadratic formula and you get the following. $t=4.937$ or $t=-5.063$.
$$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-2)\pm\sqrt{(-2)^2-4(-16)(400)}}{2(-16)}$$
Now since this is in units of time, you can disregard the negative and end up with $t=4.937$.
Then since the equation for the distance to be released is modeled by $x=91t$, just plug in for $t$ to get the distance in feet for which you should release the payload.
So you get $$t=91t=91*4.937=449.27ft$$
And that's all there is to it.