SOLUTION: When a stopper is removed from the bottom of a barrel filled with water, the depth d, in centimeters, of a liquid in the barrel can be approximated by d=0.039t^2-5.816t+200, where

Question 1130410: When a stopper is removed from the bottom of a barrel filled with water, the depth d, in centimeters, of a liquid in the barrel can be approximated by d=0.039t^2-5.816t+200, where t is the time since stopper was removed from the hole. When will the depth be 125 cm? Round to the nearest tenth of a second.
So far I have:
125=0.039t^2-5.816t+200 then I subtracted 125 from both sides so the equation is equal to 0 which will make it 0=0.039t^2-5.816t+75 I know I need to factor it but I'm not sure how to go about that. Please help. Thank you.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
When a stopper is removed from the bottom of a barrel filled with water, the depth d, in centimeters, of a liquid in the barrel can be approximated by d=0.039t^2-5.816t+200, where t is the time since stopper was removed from the hole. When will the depth be 125 cm? Round to the nearest tenth of a second.
So far I have:
125=0.039t^2-5.816t+200 then I subtracted 125 from both sides so the equation is equal to 0 which will make it 0=0.039t^2-5.816t+75 I know I need to factor it but I'm not sure how to go about that.
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0.039t^2-5.816t+75 = 0
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It might be factorable, might not.
Use the quadratic equation:
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=22.125856 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 134.869396428846, 14.258808699359. Here's your graph:

It cannot be factored, but there's another problem.
It's a parabola that opens upward, giving 2 solutions for t.
Check your equation for d.

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