-16t^2+230t-110=0

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Solution for -16t^2+230t-110=0 equation: 


Simplifying
-16t2 + 230t + -110 = 0

Reorder the terms:
-110 + 230t + -16t2 = 0

Solving
-110 + 230t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 115t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-55 + 115t + -8t2)' equal to zero and attempt to solve:

Simplifying
-55 + 115t + -8t2 = 0

Solving
-55 + 115t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
6.875 + -14.375t + t2 = 0

Move the constant term to the right:

Add '-6.875' to each side of the equation.
6.875 + -14.375t + -6.875 + t2 = 0 + -6.875

Reorder the terms:
6.875 + -6.875 + -14.375t + t2 = 0 + -6.875

Combine like terms: 6.875 + -6.875 = 0.000
0.000 + -14.375t + t2 = 0 + -6.875
-14.375t + t2 = 0 + -6.875

Combine like terms: 0 + -6.875 = -6.875
-14.375t + t2 = -6.875

The t term is -14.375t.  Take half its coefficient (-7.1875).
Square it (51.66015625) and add it to both sides.

Add '51.66015625' to each side of the equation.
-14.375t + 51.66015625 + t2 = -6.875 + 51.66015625

Reorder the terms:
51.66015625 + -14.375t + t2 = -6.875 + 51.66015625

Combine like terms: -6.875 + 51.66015625 = 44.78515625
51.66015625 + -14.375t + t2 = 44.78515625

Factor a perfect square on the left side:
(t + -7.1875)(t + -7.1875) = 44.78515625

Calculate the square root of the right side: 6.692171266

Break this problem into two subproblems by setting 
(t + -7.1875) equal to 6.692171266 and -6.692171266.


Subproblem 1
t + -7.1875 = 6.692171266

Simplifying
t + -7.1875 = 6.692171266

Reorder the terms:
-7.1875 + t = 6.692171266

Solving
-7.1875 + t = 6.692171266

Solving for variable 't'.

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

Add '7.1875' to each side of the equation.
-7.1875 + 7.1875 + t = 6.692171266 + 7.1875

Combine like terms: -7.1875 + 7.1875 = 0.0000
0.0000 + t = 6.692171266 + 7.1875
t = 6.692171266 + 7.1875

Combine like terms: 6.692171266 + 7.1875 = 13.879671266
t = 13.879671266

Simplifying
t = 13.879671266


Subproblem 2
t + -7.1875 = -6.692171266

Simplifying
t + -7.1875 = -6.692171266

Reorder the terms:
-7.1875 + t = -6.692171266

Solving
-7.1875 + t = -6.692171266

Solving for variable 't'.

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

Add '7.1875' to each side of the equation.
-7.1875 + 7.1875 + t = -6.692171266 + 7.1875

Combine like terms: -7.1875 + 7.1875 = 0.0000
0.0000 + t = -6.692171266 + 7.1875
t = -6.692171266 + 7.1875

Combine like terms: -6.692171266 + 7.1875 = 0.495328734
t = 0.495328734

Simplifying
t = 0.495328734


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {13.879671266, 0.495328734}
Solution
t = {13.879671266, 0.495328734}

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