(16t^2)+22t-112=0

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Solution for (16t^2)+22t-112=0 equation: 


Simplifying
(16t2) + 22t + -112 = 0

Reorder the terms:
-112 + 22t + (16t2) = 0

Solving
-112 + 22t + (16t2) = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + 11t + (8t2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-56 + 11t + (8t2))' equal to zero and attempt to solve:

Simplifying
-56 + 11t + (8t2) = 0

Solving
-56 + 11t + (8t2) = 0

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

Divide each side by '8'.
-7 + 1.375t + t2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 1.375t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + 1.375t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 1.375t + t2 = 0 + 7
1.375t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
1.375t + t2 = 7

The t term is 1.375t.  Take half its coefficient (0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
1.375t + 0.47265625 + t2 = 7 + 0.47265625

Reorder the terms:
0.47265625 + 1.375t + t2 = 7 + 0.47265625

Combine like terms: 7 + 0.47265625 = 7.47265625
0.47265625 + 1.375t + t2 = 7.47265625

Factor a perfect square on the left side:
((t) + 0.6875)((t) + 0.6875) = 7.47265625

Calculate the square root of the right side: 2.733615966

Break this problem into two subproblems by setting 
((t) + 0.6875) equal to 2.733615966 and -2.733615966.


Subproblem 1
(t) + 0.6875 = 2.733615966

Simplifying
(t) + 0.6875 = 2.733615966
t + 0.6875 = 2.733615966

Reorder the terms:
0.6875 + t = 2.733615966

Solving
0.6875 + t = 2.733615966

Solving for variable 't'.

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

Add '-0.6875' to each side of the equation.
0.6875 + -0.6875 + t = 2.733615966 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + t = 2.733615966 + -0.6875
t = 2.733615966 + -0.6875

Combine like terms: 2.733615966 + -0.6875 = 2.046115966
t = 2.046115966

Simplifying
t = 2.046115966


Subproblem 2
(t) + 0.6875 = -2.733615966

Simplifying
(t) + 0.6875 = -2.733615966
t + 0.6875 = -2.733615966

Reorder the terms:
0.6875 + t = -2.733615966

Solving
0.6875 + t = -2.733615966

Solving for variable 't'.

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

Add '-0.6875' to each side of the equation.
0.6875 + -0.6875 + t = -2.733615966 + -0.6875

Combine like terms: 0.6875 + -0.6875 = 0.0000
0.0000 + t = -2.733615966 + -0.6875
t = -2.733615966 + -0.6875

Combine like terms: -2.733615966 + -0.6875 = -3.421115966
t = -3.421115966

Simplifying
t = -3.421115966


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.046115966, -3.421115966}
Solution
t = {2.046115966, -3.421115966}

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