Answer:
t = 139/490 + sqrt(75671)/490 or t = 139/490 - sqrt(75671)/490
Explanation:
Solve for t:
4.9 t^2 - 2.78 t - 1.15 = 0
4.9 t^2 - 2.78 t - 1.15 = (49 t^2)/10 - (139 t)/50 - 23/20:
(49 t^2)/10 - (139 t)/50 - 23/20 = 0
Multiply both sides by 10/49:
t^2 - (139 t)/245 - 23/98 = 0
Add 23/98 to both sides:
t^2 - (139 t)/245 = 23/98
Add 19321/240100 to both sides:
t^2 - (139 t)/245 + 19321/240100 = 75671/240100
Write the left hand side as a square:
(t - 139/490)^2 = 75671/240100
Take the square root of both sides:
t - 139/490 = sqrt(75671)/490 or t - 139/490 = -sqrt(75671)/490
Add 139/490 to both sides:
t = 139/490 + sqrt(75671)/490 or t - 139/490 = -sqrt(75671)/490
Add 139/490 to both sides:
Answer: t = 139/490 + sqrt(75671)/490 or t = 139/490 - sqrt(75671)/490