128t-6t^2=112

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Solution for 128t-6t^2=112 equation: 


Simplifying
128t + -6t2 = 112

Solving
128t + -6t2 = 112

Solving for variable 't'.

Reorder the terms:
-112 + 128t + -6t2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + 128t + -6t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + 64t + -3t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-56 + 64t + -3t2)' equal to zero and attempt to solve:

Simplifying
-56 + 64t + -3t2 = 0

Solving
-56 + 64t + -3t2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
18.66666667 + -21.33333333t + t2 = 0

Move the constant term to the right:

Add '-18.66666667' to each side of the equation.
18.66666667 + -21.33333333t + -18.66666667 + t2 = 0 + -18.66666667

Reorder the terms:
18.66666667 + -18.66666667 + -21.33333333t + t2 = 0 + -18.66666667

Combine like terms: 18.66666667 + -18.66666667 = 0.00000000
0.00000000 + -21.33333333t + t2 = 0 + -18.66666667
-21.33333333t + t2 = 0 + -18.66666667

Combine like terms: 0 + -18.66666667 = -18.66666667
-21.33333333t + t2 = -18.66666667

The t term is -21.33333333t.  Take half its coefficient (-10.66666667).
Square it (113.7777778) and add it to both sides.

Add '113.7777778' to each side of the equation.
-21.33333333t + 113.7777778 + t2 = -18.66666667 + 113.7777778

Reorder the terms:
113.7777778 + -21.33333333t + t2 = -18.66666667 + 113.7777778

Combine like terms: -18.66666667 + 113.7777778 = 95.11111113
113.7777778 + -21.33333333t + t2 = 95.11111113

Factor a perfect square on the left side:
(t + -10.66666667)(t + -10.66666667) = 95.11111113

Calculate the square root of the right side: 9.75249256

Break this problem into two subproblems by setting 
(t + -10.66666667) equal to 9.75249256 and -9.75249256.


Subproblem 1
t + -10.66666667 = 9.75249256

Simplifying
t + -10.66666667 = 9.75249256

Reorder the terms:
-10.66666667 + t = 9.75249256

Solving
-10.66666667 + t = 9.75249256

Solving for variable 't'.

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

Add '10.66666667' to each side of the equation.
-10.66666667 + 10.66666667 + t = 9.75249256 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + t = 9.75249256 + 10.66666667
t = 9.75249256 + 10.66666667

Combine like terms: 9.75249256 + 10.66666667 = 20.41915923
t = 20.41915923

Simplifying
t = 20.41915923


Subproblem 2
t + -10.66666667 = -9.75249256

Simplifying
t + -10.66666667 = -9.75249256

Reorder the terms:
-10.66666667 + t = -9.75249256

Solving
-10.66666667 + t = -9.75249256

Solving for variable 't'.

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

Add '10.66666667' to each side of the equation.
-10.66666667 + 10.66666667 + t = -9.75249256 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + t = -9.75249256 + 10.66666667
t = -9.75249256 + 10.66666667

Combine like terms: -9.75249256 + 10.66666667 = 0.91417411
t = 0.91417411

Simplifying
t = 0.91417411


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {20.41915923, 0.91417411}
Solution
t = {20.41915923, 0.91417411}

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