When Daniel's head reaches the surface, h(t) = 0
Therefore:
-8t² - 28t + 60 = 0 To simplify, divide both sides by -4
2t² + 7t - 15 = 0
Consider the trinomial ax² + bx + c
To factor by grouping, we must find two numbers that multiply to equal AC (-30) and add up to B (7)
Two numbers that satisfy this are 10 and -3:
2t² + 10t - 3t - 15 = 0 Rewrite the equation using 10t and -3t
2t (t + 5) -3 (t +5) = 0 Regroup, then rewrite
(2t -3) (t+5) = 0
2t-3 = 0
2t = 3
t = 3/2
OR
t + 5 = 0
t = -5
We know t cannot be a negative number, so the answer is:
t = 3/2, or 1 and a half seconds
