-11.5+29t-16t^2=0

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Solution for -11.5+29t-16t^2=0 equation: 


Simplifying
-11.5 + 29t + -16t2 = 0

Solving
-11.5 + 29t + -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'.
0.71875 + -1.8125t + t2 = 0

Move the constant term to the right:

Add '-0.71875' to each side of the equation.
0.71875 + -1.8125t + -0.71875 + t2 = 0 + -0.71875

Reorder the terms:
0.71875 + -0.71875 + -1.8125t + t2 = 0 + -0.71875

Combine like terms: 0.71875 + -0.71875 = 0.00000
0.00000 + -1.8125t + t2 = 0 + -0.71875
-1.8125t + t2 = 0 + -0.71875

Combine like terms: 0 + -0.71875 = -0.71875
-1.8125t + t2 = -0.71875

The t term is -1.8125t.  Take half its coefficient (-0.90625).
Square it (0.8212890625) and add it to both sides.

Add '0.8212890625' to each side of the equation.
-1.8125t + 0.8212890625 + t2 = -0.71875 + 0.8212890625

Reorder the terms:
0.8212890625 + -1.8125t + t2 = -0.71875 + 0.8212890625

Combine like terms: -0.71875 + 0.8212890625 = 0.1025390625
0.8212890625 + -1.8125t + t2 = 0.1025390625

Factor a perfect square on the left side:
(t + -0.90625)(t + -0.90625) = 0.1025390625

Calculate the square root of the right side: 0.320217211

Break this problem into two subproblems by setting 
(t + -0.90625) equal to 0.320217211 and -0.320217211.


Subproblem 1
t + -0.90625 = 0.320217211

Simplifying
t + -0.90625 = 0.320217211

Reorder the terms:
-0.90625 + t = 0.320217211

Solving
-0.90625 + t = 0.320217211

Solving for variable 't'.

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

Add '0.90625' to each side of the equation.
-0.90625 + 0.90625 + t = 0.320217211 + 0.90625

Combine like terms: -0.90625 + 0.90625 = 0.00000
0.00000 + t = 0.320217211 + 0.90625
t = 0.320217211 + 0.90625

Combine like terms: 0.320217211 + 0.90625 = 1.226467211
t = 1.226467211

Simplifying
t = 1.226467211


Subproblem 2
t + -0.90625 = -0.320217211

Simplifying
t + -0.90625 = -0.320217211

Reorder the terms:
-0.90625 + t = -0.320217211

Solving
-0.90625 + t = -0.320217211

Solving for variable 't'.

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

Add '0.90625' to each side of the equation.
-0.90625 + 0.90625 + t = -0.320217211 + 0.90625

Combine like terms: -0.90625 + 0.90625 = 0.00000
0.00000 + t = -0.320217211 + 0.90625
t = -0.320217211 + 0.90625

Combine like terms: -0.320217211 + 0.90625 = 0.586032789
t = 0.586032789

Simplifying
t = 0.586032789


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.226467211, 0.586032789}

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