-16t^2+65.5t+5.5=0

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Solution for -16t^2+65.5t+5.5=0 equation: 


Simplifying
-16t2 + 65.5t + 5.5 = 0

Reorder the terms:
5.5 + 65.5t + -16t2 = 0

Solving
5.5 + 65.5t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.34375 + -4.09375t + t2 = 0

Move the constant term to the right:

Add '0.34375' to each side of the equation.
-0.34375 + -4.09375t + 0.34375 + t2 = 0 + 0.34375

Reorder the terms:
-0.34375 + 0.34375 + -4.09375t + t2 = 0 + 0.34375

Combine like terms: -0.34375 + 0.34375 = 0.00000
0.00000 + -4.09375t + t2 = 0 + 0.34375
-4.09375t + t2 = 0 + 0.34375

Combine like terms: 0 + 0.34375 = 0.34375
-4.09375t + t2 = 0.34375

The t term is -4.09375t.  Take half its coefficient (-2.046875).
Square it (4.189697266) and add it to both sides.

Add '4.189697266' to each side of the equation.
-4.09375t + 4.189697266 + t2 = 0.34375 + 4.189697266

Reorder the terms:
4.189697266 + -4.09375t + t2 = 0.34375 + 4.189697266

Combine like terms: 0.34375 + 4.189697266 = 4.533447266
4.189697266 + -4.09375t + t2 = 4.533447266

Factor a perfect square on the left side:
(t + -2.046875)(t + -2.046875) = 4.533447266

Calculate the square root of the right side: 2.129189345

Break this problem into two subproblems by setting 
(t + -2.046875) equal to 2.129189345 and -2.129189345.


Subproblem 1
t + -2.046875 = 2.129189345

Simplifying
t + -2.046875 = 2.129189345

Reorder the terms:
-2.046875 + t = 2.129189345

Solving
-2.046875 + t = 2.129189345

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '2.046875' to each side of the equation.
-2.046875 + 2.046875 + t = 2.129189345 + 2.046875

Combine like terms: -2.046875 + 2.046875 = 0.000000
0.000000 + t = 2.129189345 + 2.046875
t = 2.129189345 + 2.046875

Combine like terms: 2.129189345 + 2.046875 = 4.176064345
t = 4.176064345

Simplifying
t = 4.176064345


Subproblem 2
t + -2.046875 = -2.129189345

Simplifying
t + -2.046875 = -2.129189345

Reorder the terms:
-2.046875 + t = -2.129189345

Solving
-2.046875 + t = -2.129189345

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '2.046875' to each side of the equation.
-2.046875 + 2.046875 + t = -2.129189345 + 2.046875

Combine like terms: -2.046875 + 2.046875 = 0.000000
0.000000 + t = -2.129189345 + 2.046875
t = -2.129189345 + 2.046875

Combine like terms: -2.129189345 + 2.046875 = -0.082314345
t = -0.082314345

Simplifying
t = -0.082314345


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.176064345, -0.082314345}

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