SOLUTION: I need to solve this by factoring but can't seem to get it! Suppose the altitude of a rising hot air balloon is given by h=0.04t^2+2t where "t" is the time in seconds afer the b

Question 212927: I need to solve this by factoring but can't seem to get it!
Suppose the altitude of a rising hot air balloon is given by h=0.04t^2+2t where "t" is the time in seconds afer the balloon leaves the ground. How long will it take for the balloon to reach an altitude of 200 ft.?
Thanks for the help!

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
First, substitute the height of 200 feet for h in the equation:

200=0.04t^2 +2t

Since it's a quadratic equation, set it equal to zero by subtracting 200 from each side:
0=0.04t^2 + 2t -200

Next I would get rid of that ugly decimal by multiplying both sides by 100:
0= 4t^2 + 200t - 20000

Divide both sides by 4:
0=t^2 + 50t -5000

Next, to solve by factoring you must find two numbers with opposite sign whose product is 5000 (actually -5000!) and whose difference is 50 (to give you the middle term of +50t). The first combination of numbers that came to mind for me was 50*100. That's the one!!

0=(t+100)(t-50)
t=-100 or t=50

Reject the negative answer, since time cannot be negative, and the answer must be t=50 sec.

R^2

Dr. Robert J. Rapalje
Seminole Community College
Altamonte Springs Campus
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