B (t) = 80t-16t^2+3.5 solve for t

t = 5/2 + (3 sqrt (23/2)) / 4 or t = 5/2 - (3 sqrt (23/2)) / 4

Step-by-step 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