16t^2+44t-24=0

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Solution for 16t^2+44t-24=0 equation: 


Simplifying
16t2 + 44t + -24 = 0

Reorder the terms:
-24 + 44t + 16t2 = 0

Solving
-24 + 44t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + 11t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-6 + 11t + 4t2)' equal to zero and attempt to solve:

Simplifying
-6 + 11t + 4t2 = 0

Solving
-6 + 11t + 4t2 = 0

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

Divide each side by '4'.
-1.5 + 2.75t + t2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2.75t + 1.5 + t2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2.75t + t2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2.75t + t2 = 0 + 1.5
2.75t + t2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2.75t + t2 = 1.5

The t term is 2.75t.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75t + 1.890625 + t2 = 1.5 + 1.890625

Reorder the terms:
1.890625 + 2.75t + t2 = 1.5 + 1.890625

Combine like terms: 1.5 + 1.890625 = 3.390625
1.890625 + 2.75t + t2 = 3.390625

Factor a perfect square on the left side:
(t + 1.375)(t + 1.375) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(t + 1.375) equal to 1.841364983 and -1.841364983.


Subproblem 1
t + 1.375 = 1.841364983

Simplifying
t + 1.375 = 1.841364983

Reorder the terms:
1.375 + t = 1.841364983

Solving
1.375 + t = 1.841364983

Solving for variable 't'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + t = 1.841364983 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + t = 1.841364983 + -1.375
t = 1.841364983 + -1.375

Combine like terms: 1.841364983 + -1.375 = 0.466364983
t = 0.466364983

Simplifying
t = 0.466364983


Subproblem 2
t + 1.375 = -1.841364983

Simplifying
t + 1.375 = -1.841364983

Reorder the terms:
1.375 + t = -1.841364983

Solving
1.375 + t = -1.841364983

Solving for variable 't'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + t = -1.841364983 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + t = -1.841364983 + -1.375
t = -1.841364983 + -1.375

Combine like terms: -1.841364983 + -1.375 = -3.216364983
t = -3.216364983

Simplifying
t = -3.216364983


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.466364983, -3.216364983}
Solution
t = {0.466364983, -3.216364983}

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