SOLUTION: A foul ball leaves a bat, hits home plate, and travels straight up with an initial volocity of the rebound of 64 ft/s. How many seconds later will the ball be 64 ft above the grou

Question 395136: A foul ball leaves a bat, hits home plate, and travels straight up with an initial volocity of the rebound of 64 ft/s. How many seconds later will the ball be 64 ft above the ground.I figured it out till I factored out the 16 and then got lost.
H=64t-16t^2
64=64t-16t^2 has 64 subtracted from both sides and becomes the following:
0=-16t^2+64t-64
0=16(t^2+4t-4)
I saw that the first and last terms were squares and so tried to see if it were a perfect square trinomial: (t-2)^2
but when I started the checking process the 2t(-2)=-4 but our middle term is positive four so it isn't a perfect square trinomial, I included right here how I began to check to see if the middle term would come out recalling the pattern for finding the square of a binomial, square of the first term, twice the product of the two terms, square of the last term(Courtesy.,Introductory Algebra: An Applied Approach (a+b)^2+a^2+2ab+b^2
so following what I spoke of above my problem looked like this(t)2+2(t)(-2)-(2)^2but I realized while lookingat the final term, that the final term if -(2)^2 would be -2*-2=4 not the negative four I needed.
So the second thing I started was trying out the different combination of numbers-but became confused because I needed to have a negative 2 and a positive 2 to come out with a negative four but when plugged in (t+2)(t-2)comes to zero and not the positive four I need. I tried +4-1 and vice versa and nothing worked out so I figured I had done something wrong somewhere
Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A foul ball leaves a bat, hits home plate, and travels straight up with an initial volocity of the rebound of 64 ft/s. How many seconds later will the ball be 64 ft above the ground.I figured it out till I factored out the 16 and then got lost.
H=64t-16t^2
64=64t-16t^2 has 64 subtracted from both sides and becomes the following:
0=-16t^2+64t-64
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Comment: You ignored the negative on the 16.
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0 = -16(t^2-4t+4)
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t^2-4t+4 = 0
(t-2) = 0
t = 2
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Cheers,
Stan H.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let's start at:
Factor a -16 and note the sign changes!
so according to the zero product property, we have:
or Factor!
so...
seconds.
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