16t^2+72t+2=0

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Solution for 16t^2+72t+2=0 equation: 


Simplifying
16t2 + 72t + 2 = 0

Reorder the terms:
2 + 72t + 16t2 = 0

Solving
2 + 72t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 36t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 36t + 8t2)' equal to zero and attempt to solve:

Simplifying
1 + 36t + 8t2 = 0

Solving
1 + 36t + 8t2 = 0

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

Divide each side by '8'.
0.125 + 4.5t + t2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 4.5t + -0.125 + t2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 4.5t + t2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 4.5t + t2 = 0 + -0.125
4.5t + t2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
4.5t + t2 = -0.125

The t term is 4.5t.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5t + 5.0625 + t2 = -0.125 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = -0.125 + 5.0625

Combine like terms: -0.125 + 5.0625 = 4.9375
5.0625 + 4.5t + t2 = 4.9375

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 4.9375

Calculate the square root of the right side: 2.222048604

Break this problem into two subproblems by setting 
(t + 2.25) equal to 2.222048604 and -2.222048604.


Subproblem 1
t + 2.25 = 2.222048604

Simplifying
t + 2.25 = 2.222048604

Reorder the terms:
2.25 + t = 2.222048604

Solving
2.25 + t = 2.222048604

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = 2.222048604 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 2.222048604 + -2.25
t = 2.222048604 + -2.25

Combine like terms: 2.222048604 + -2.25 = -0.027951396
t = -0.027951396

Simplifying
t = -0.027951396


Subproblem 2
t + 2.25 = -2.222048604

Simplifying
t + 2.25 = -2.222048604

Reorder the terms:
2.25 + t = -2.222048604

Solving
2.25 + t = -2.222048604

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = -2.222048604 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -2.222048604 + -2.25
t = -2.222048604 + -2.25

Combine like terms: -2.222048604 + -2.25 = -4.472048604
t = -4.472048604

Simplifying
t = -4.472048604


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.027951396, -4.472048604}
Solution
t = {-0.027951396, -4.472048604}

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