-16t^2+110t-185=0

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Solution for -16t^2+110t-185=0 equation: 


Simplifying
-16t2 + 110t + -185 = 0

Reorder the terms:
-185 + 110t + -16t2 = 0

Solving
-185 + 110t + -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'.
11.5625 + -6.875t + t2 = 0

Move the constant term to the right:

Add '-11.5625' to each side of the equation.
11.5625 + -6.875t + -11.5625 + t2 = 0 + -11.5625

Reorder the terms:
11.5625 + -11.5625 + -6.875t + t2 = 0 + -11.5625

Combine like terms: 11.5625 + -11.5625 = 0.0000
0.0000 + -6.875t + t2 = 0 + -11.5625
-6.875t + t2 = 0 + -11.5625

Combine like terms: 0 + -11.5625 = -11.5625
-6.875t + t2 = -11.5625

The t term is -6.875t.  Take half its coefficient (-3.4375).
Square it (11.81640625) and add it to both sides.

Add '11.81640625' to each side of the equation.
-6.875t + 11.81640625 + t2 = -11.5625 + 11.81640625

Reorder the terms:
11.81640625 + -6.875t + t2 = -11.5625 + 11.81640625

Combine like terms: -11.5625 + 11.81640625 = 0.25390625
11.81640625 + -6.875t + t2 = 0.25390625

Factor a perfect square on the left side:
(t + -3.4375)(t + -3.4375) = 0.25390625

Calculate the square root of the right side: 0.503891109

Break this problem into two subproblems by setting 
(t + -3.4375) equal to 0.503891109 and -0.503891109.


Subproblem 1
t + -3.4375 = 0.503891109

Simplifying
t + -3.4375 = 0.503891109

Reorder the terms:
-3.4375 + t = 0.503891109

Solving
-3.4375 + t = 0.503891109

Solving for variable 't'.

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

Add '3.4375' to each side of the equation.
-3.4375 + 3.4375 + t = 0.503891109 + 3.4375

Combine like terms: -3.4375 + 3.4375 = 0.0000
0.0000 + t = 0.503891109 + 3.4375
t = 0.503891109 + 3.4375

Combine like terms: 0.503891109 + 3.4375 = 3.941391109
t = 3.941391109

Simplifying
t = 3.941391109


Subproblem 2
t + -3.4375 = -0.503891109

Simplifying
t + -3.4375 = -0.503891109

Reorder the terms:
-3.4375 + t = -0.503891109

Solving
-3.4375 + t = -0.503891109

Solving for variable 't'.

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

Add '3.4375' to each side of the equation.
-3.4375 + 3.4375 + t = -0.503891109 + 3.4375

Combine like terms: -3.4375 + 3.4375 = 0.0000
0.0000 + t = -0.503891109 + 3.4375
t = -0.503891109 + 3.4375

Combine like terms: -0.503891109 + 3.4375 = 2.933608891
t = 2.933608891

Simplifying
t = 2.933608891


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.941391109, 2.933608891}

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