19.6788t^2-128.988t+125.12=0

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Solution for 19.6788t^2-128.988t+125.12=0 equation: 


Simplifying
19.6788t2 + -128.988t + 125.12 = 0

Reorder the terms:
125.12 + -128.988t + 19.6788t2 = 0

Solving
125.12 + -128.988t + 19.6788t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
19.6788 the coefficient of the squared term: 

Divide each side by '19.6788'.
6.358111267 + -6.554667968t + t2 = 0

Move the constant term to the right:

Add '-6.358111267' to each side of the equation.
6.358111267 + -6.554667968t + -6.358111267 + t2 = 0 + -6.358111267

Reorder the terms:
6.358111267 + -6.358111267 + -6.554667968t + t2 = 0 + -6.358111267

Combine like terms: 6.358111267 + -6.358111267 = 0.000000000
0.000000000 + -6.554667968t + t2 = 0 + -6.358111267
-6.554667968t + t2 = 0 + -6.358111267

Combine like terms: 0 + -6.358111267 = -6.358111267
-6.554667968t + t2 = -6.358111267

The t term is -6.554667968t.  Take half its coefficient (-3.277333984).
Square it (10.74091804) and add it to both sides.

Add '10.74091804' to each side of the equation.
-6.554667968t + 10.74091804 + t2 = -6.358111267 + 10.74091804

Reorder the terms:
10.74091804 + -6.554667968t + t2 = -6.358111267 + 10.74091804

Combine like terms: -6.358111267 + 10.74091804 = 4.382806773
10.74091804 + -6.554667968t + t2 = 4.382806773

Factor a perfect square on the left side:
(t + -3.277333984)(t + -3.277333984) = 4.382806773

Calculate the square root of the right side: 2.09351541

Break this problem into two subproblems by setting 
(t + -3.277333984) equal to 2.09351541 and -2.09351541.


Subproblem 1
t + -3.277333984 = 2.09351541

Simplifying
t + -3.277333984 = 2.09351541

Reorder the terms:
-3.277333984 + t = 2.09351541

Solving
-3.277333984 + t = 2.09351541

Solving for variable 't'.

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

Add '3.277333984' to each side of the equation.
-3.277333984 + 3.277333984 + t = 2.09351541 + 3.277333984

Combine like terms: -3.277333984 + 3.277333984 = 0.000000000
0.000000000 + t = 2.09351541 + 3.277333984
t = 2.09351541 + 3.277333984

Combine like terms: 2.09351541 + 3.277333984 = 5.370849394
t = 5.370849394

Simplifying
t = 5.370849394


Subproblem 2
t + -3.277333984 = -2.09351541

Simplifying
t + -3.277333984 = -2.09351541

Reorder the terms:
-3.277333984 + t = -2.09351541

Solving
-3.277333984 + t = -2.09351541

Solving for variable 't'.

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

Add '3.277333984' to each side of the equation.
-3.277333984 + 3.277333984 + t = -2.09351541 + 3.277333984

Combine like terms: -3.277333984 + 3.277333984 = 0.000000000
0.000000000 + t = -2.09351541 + 3.277333984
t = -2.09351541 + 3.277333984

Combine like terms: -2.09351541 + 3.277333984 = 1.183818574
t = 1.183818574

Simplifying
t = 1.183818574


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.370849394, 1.183818574}

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