If a rocket is propelled upward from ground level, it's height in meters after t seconds is given by h=-9.8t^2+88.2t. During what interval of time will the rocket be higher than 137.2m?

h=9.8t^2+ 88.2t
I divided both sides by -9.8 which gave me

But I can't remember what step is next please help. Thanks in advance:-)

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  1. The equation:
    137.2 = -9.8t^2 + 88.2t

    Divide both sides by -9.8 (whatever operation you do to one side of an equation you must do to the other side as well):

    (137.2)/-9.8 = (-9.8t^2 + 88.2t)/-9.8

    -14 = t^2 - 9

    Set the equation equal to 0:

    0 = t^2 - 9 + 14

    Try to factor:

    0 = (t - 7)(t - 2)

    Set the factors equal to 0:
    t - 7 = 0
    t - 2 = 0

    Therefore, the two solutions are t = 2 and t = 7.

    Interval: 2 < t < 7

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