16t^2+128t+2=0

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Solution for 16t^2+128t+2=0 equation: 


Simplifying
16t2 + 128t + 2 = 0

Reorder the terms:
2 + 128t + 16t2 = 0

Solving
2 + 128t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 64t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 64t + 8t2)' equal to zero and attempt to solve:

Simplifying
1 + 64t + 8t2 = 0

Solving
1 + 64t + 8t2 = 0

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

Divide each side by '8'.
0.125 + 8t + t2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 8t + -0.125 + t2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 8t + t2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 8t + t2 = 0 + -0.125
8t + t2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
8t + t2 = -0.125

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = -0.125 + 16

Reorder the terms:
16 + 8t + t2 = -0.125 + 16

Combine like terms: -0.125 + 16 = 15.875
16 + 8t + t2 = 15.875

Factor a perfect square on the left side:
(t + 4)(t + 4) = 15.875

Calculate the square root of the right side: 3.984344363

Break this problem into two subproblems by setting 
(t + 4) equal to 3.984344363 and -3.984344363.


Subproblem 1
t + 4 = 3.984344363

Simplifying
t + 4 = 3.984344363

Reorder the terms:
4 + t = 3.984344363

Solving
4 + t = 3.984344363

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 3.984344363 + -4

Combine like terms: 4 + -4 = 0
0 + t = 3.984344363 + -4
t = 3.984344363 + -4

Combine like terms: 3.984344363 + -4 = -0.015655637
t = -0.015655637

Simplifying
t = -0.015655637


Subproblem 2
t + 4 = -3.984344363

Simplifying
t + 4 = -3.984344363

Reorder the terms:
4 + t = -3.984344363

Solving
4 + t = -3.984344363

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -3.984344363 + -4

Combine like terms: 4 + -4 = 0
0 + t = -3.984344363 + -4
t = -3.984344363 + -4

Combine like terms: -3.984344363 + -4 = -7.984344363
t = -7.984344363

Simplifying
t = -7.984344363


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.015655637, -7.984344363}
Solution
t = {-0.015655637, -7.984344363}

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