-16t^2-74t-6=0

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Solution for -16t^2-74t-6=0 equation: 


Simplifying
-16t2 + -74t + -6 = 0

Reorder the terms:
-6 + -74t + -16t2 = 0

Solving
-6 + -74t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 37t + 8t2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(3 + 37t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + 37t + 8t2 = 0

Solving
3 + 37t + 8t2 = 0

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

Divide each side by '8'.
0.375 + 4.625t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 4.625t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 4.625t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 4.625t + t2 = 0 + -0.375
4.625t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
4.625t + t2 = -0.375

The t term is 4.625t.  Take half its coefficient (2.3125).
Square it (5.34765625) and add it to both sides.

Add '5.34765625' to each side of the equation.
4.625t + 5.34765625 + t2 = -0.375 + 5.34765625

Reorder the terms:
5.34765625 + 4.625t + t2 = -0.375 + 5.34765625

Combine like terms: -0.375 + 5.34765625 = 4.97265625
5.34765625 + 4.625t + t2 = 4.97265625

Factor a perfect square on the left side:
(t + 2.3125)(t + 2.3125) = 4.97265625

Calculate the square root of the right side: 2.229945347

Break this problem into two subproblems by setting 
(t + 2.3125) equal to 2.229945347 and -2.229945347.


Subproblem 1
t + 2.3125 = 2.229945347

Simplifying
t + 2.3125 = 2.229945347

Reorder the terms:
2.3125 + t = 2.229945347

Solving
2.3125 + t = 2.229945347

Solving for variable 't'.

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

Add '-2.3125' to each side of the equation.
2.3125 + -2.3125 + t = 2.229945347 + -2.3125

Combine like terms: 2.3125 + -2.3125 = 0.0000
0.0000 + t = 2.229945347 + -2.3125
t = 2.229945347 + -2.3125

Combine like terms: 2.229945347 + -2.3125 = -0.082554653
t = -0.082554653

Simplifying
t = -0.082554653


Subproblem 2
t + 2.3125 = -2.229945347

Simplifying
t + 2.3125 = -2.229945347

Reorder the terms:
2.3125 + t = -2.229945347

Solving
2.3125 + t = -2.229945347

Solving for variable 't'.

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

Add '-2.3125' to each side of the equation.
2.3125 + -2.3125 + t = -2.229945347 + -2.3125

Combine like terms: 2.3125 + -2.3125 = 0.0000
0.0000 + t = -2.229945347 + -2.3125
t = -2.229945347 + -2.3125

Combine like terms: -2.229945347 + -2.3125 = -4.542445347
t = -4.542445347

Simplifying
t = -4.542445347


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.082554653, -4.542445347}
Solution
t = {-0.082554653, -4.542445347}

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