Answer:
t = 5/2 + (3 sqrt(23/2))/4 or t = 5/2 - (3 sqrt(23/2))/4
Explanation:
Solve for t:
-16 t^2 + 80 t + 3.5 = 0
-16 t^2 + 80 t + 3.5 = -16 t^2 + 80 t + 7/2:
-16 t^2 + 80 t + 7/2 = 0
Divide both sides by -16:
t^2 - 5 t - 7/32 = 0
Add 7/32 to both sides:
t^2 - 5 t = 7/32
Add 25/4 to both sides:
t^2 - 5 t + 25/4 = 207/32
Write the left hand side as a square:
(t - 5/2)^2 = 207/32
Take the square root of both sides:
t - 5/2 = (3 sqrt(23/2))/4 or t - 5/2 = -(3 sqrt(23/2))/4
Add 5/2 to both sides:
t = 5/2 + (3 sqrt(23/2))/4 or t - 5/2 = -(3 sqrt(23/2))/4
Add 5/2 to both sides:
Answer: t = 5/2 + (3 sqrt(23/2))/4 or t = 5/2 - (3 sqrt(23/2))/4