190=16t^2-110t-190

Solution for 190=16t^2-110t-190 equation:

Simplifying
190 = 16t2 + -110t + -190

Reorder the terms:
190 = -190 + -110t + 16t2

Solving
190 = -190 + -110t + 16t2

Solving for variable 't'.

Combine like terms: 190 + 190 = 380
380 + 110t + -16t2 = -190 + -110t + 16t2 + 190 + 110t + -16t2

Reorder the terms:
380 + 110t + -16t2 = -190 + 190 + -110t + 110t + 16t2 + -16t2

Combine like terms: -190 + 190 = 0
380 + 110t + -16t2 = 0 + -110t + 110t + 16t2 + -16t2
380 + 110t + -16t2 = -110t + 110t + 16t2 + -16t2

Combine like terms: -110t + 110t = 0
380 + 110t + -16t2 = 0 + 16t2 + -16t2
380 + 110t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
380 + 110t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(190 + 55t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(190 + 55t + -8t2)' equal to zero and attempt to solve:

Simplifying
190 + 55t + -8t2 = 0

Solving
190 + 55t + -8t2 = 0

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

Divide each side by '-8'.
-23.75 + -6.875t + t2 = 0

Move the constant term to the right:

Add '23.75' to each side of the equation.
-23.75 + -6.875t + 23.75 + t2 = 0 + 23.75

Reorder the terms:
-23.75 + 23.75 + -6.875t + t2 = 0 + 23.75

Combine like terms: -23.75 + 23.75 = 0.00
0.00 + -6.875t + t2 = 0 + 23.75
-6.875t + t2 = 0 + 23.75

Combine like terms: 0 + 23.75 = 23.75
-6.875t + t2 = 23.75

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 = 23.75 + 11.81640625

Reorder the terms:
11.81640625 + -6.875t + t2 = 23.75 + 11.81640625

Combine like terms: 23.75 + 11.81640625 = 35.56640625
11.81640625 + -6.875t + t2 = 35.56640625

Factor a perfect square on the left side:
(t + -3.4375)(t + -3.4375) = 35.56640625

Calculate the square root of the right side: 5.963757729

Break this problem into two subproblems by setting 
(t + -3.4375) equal to 5.963757729 and -5.963757729.

Subproblem 1
t + -3.4375 = 5.963757729

Simplifying
t + -3.4375 = 5.963757729

Reorder the terms:
-3.4375 + t = 5.963757729

Solving
-3.4375 + t = 5.963757729

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 = 5.963757729 + 3.4375

Combine like terms: -3.4375 + 3.4375 = 0.0000
0.0000 + t = 5.963757729 + 3.4375
t = 5.963757729 + 3.4375

Combine like terms: 5.963757729 + 3.4375 = 9.401257729
t = 9.401257729

Simplifying
t = 9.401257729

Subproblem 2
t + -3.4375 = -5.963757729

Simplifying
t + -3.4375 = -5.963757729

Reorder the terms:
-3.4375 + t = -5.963757729

Solving
-3.4375 + t = -5.963757729

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 = -5.963757729 + 3.4375

Combine like terms: -3.4375 + 3.4375 = 0.0000
0.0000 + t = -5.963757729 + 3.4375
t = -5.963757729 + 3.4375

Combine like terms: -5.963757729 + 3.4375 = -2.526257729
t = -2.526257729

Simplifying
t = -2.526257729

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.401257729, -2.526257729}
Solution
t = {9.401257729, -2.526257729}