16t^2+104t+56=0

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Solution for 16t^2+104t+56=0 equation: 


Simplifying
16t2 + 104t + 56 = 0

Reorder the terms:
56 + 104t + 16t2 = 0

Solving
56 + 104t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(7 + 13t + 2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(7 + 13t + 2t2)' equal to zero and attempt to solve:

Simplifying
7 + 13t + 2t2 = 0

Solving
7 + 13t + 2t2 = 0

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

Divide each side by '2'.
3.5 + 6.5t + t2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 6.5t + -3.5 + t2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 6.5t + t2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 6.5t + t2 = 0 + -3.5
6.5t + t2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
6.5t + t2 = -3.5

The t term is 6.5t.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5t + 10.5625 + t2 = -3.5 + 10.5625

Reorder the terms:
10.5625 + 6.5t + t2 = -3.5 + 10.5625

Combine like terms: -3.5 + 10.5625 = 7.0625
10.5625 + 6.5t + t2 = 7.0625

Factor a perfect square on the left side:
(t + 3.25)(t + 3.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(t + 3.25) equal to 2.657536453 and -2.657536453.


Subproblem 1
t + 3.25 = 2.657536453

Simplifying
t + 3.25 = 2.657536453

Reorder the terms:
3.25 + t = 2.657536453

Solving
3.25 + t = 2.657536453

Solving for variable 't'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + t = 2.657536453 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + t = 2.657536453 + -3.25
t = 2.657536453 + -3.25

Combine like terms: 2.657536453 + -3.25 = -0.592463547
t = -0.592463547

Simplifying
t = -0.592463547


Subproblem 2
t + 3.25 = -2.657536453

Simplifying
t + 3.25 = -2.657536453

Reorder the terms:
3.25 + t = -2.657536453

Solving
3.25 + t = -2.657536453

Solving for variable 't'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + t = -2.657536453 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + t = -2.657536453 + -3.25
t = -2.657536453 + -3.25

Combine like terms: -2.657536453 + -3.25 = -5.907536453
t = -5.907536453

Simplifying
t = -5.907536453


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.592463547, -5.907536453}
Solution
t = {-0.592463547, -5.907536453}

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