=16t^2+96t+4

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Solution for =16t^2+96t+4 equation: 


Simplifying
0 = 16t2 + 96t + 4

Reorder the terms:
0 = 4 + 96t + 16t2

Solving
0 = 4 + 96t + 16t2

Solving for variable 't'.

Combine like terms: 0 + -4 = -4
-4 + -96t + -16t2 = 4 + 96t + 16t2 + -4 + -96t + -16t2

Reorder the terms:
-4 + -96t + -16t2 = 4 + -4 + 96t + -96t + 16t2 + -16t2

Combine like terms: 4 + -4 = 0
-4 + -96t + -16t2 = 0 + 96t + -96t + 16t2 + -16t2
-4 + -96t + -16t2 = 96t + -96t + 16t2 + -16t2

Combine like terms: 96t + -96t = 0
-4 + -96t + -16t2 = 0 + 16t2 + -16t2
-4 + -96t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-4 + -96t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(1 + 24t + 4t2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(1 + 24t + 4t2)' equal to zero and attempt to solve:

Simplifying
1 + 24t + 4t2 = 0

Solving
1 + 24t + 4t2 = 0

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

Divide each side by '4'.
0.25 + 6t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 6t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 6t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 6t + t2 = 0 + -0.25
6t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
6t + t2 = -0.25

The t term is 6t.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6t + 9 + t2 = -0.25 + 9

Reorder the terms:
9 + 6t + t2 = -0.25 + 9

Combine like terms: -0.25 + 9 = 8.75
9 + 6t + t2 = 8.75

Factor a perfect square on the left side:
(t + 3)(t + 3) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(t + 3) equal to 2.958039892 and -2.958039892.


Subproblem 1
t + 3 = 2.958039892

Simplifying
t + 3 = 2.958039892

Reorder the terms:
3 + t = 2.958039892

Solving
3 + t = 2.958039892

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = 2.958039892 + -3

Combine like terms: 3 + -3 = 0
0 + t = 2.958039892 + -3
t = 2.958039892 + -3

Combine like terms: 2.958039892 + -3 = -0.041960108
t = -0.041960108

Simplifying
t = -0.041960108


Subproblem 2
t + 3 = -2.958039892

Simplifying
t + 3 = -2.958039892

Reorder the terms:
3 + t = -2.958039892

Solving
3 + t = -2.958039892

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = -2.958039892 + -3

Combine like terms: 3 + -3 = 0
0 + t = -2.958039892 + -3
t = -2.958039892 + -3

Combine like terms: -2.958039892 + -3 = -5.958039892
t = -5.958039892

Simplifying
t = -5.958039892


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.041960108, -5.958039892}
Solution
t = {-0.041960108, -5.958039892}

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