-16t^2-12t+52=0

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Solution for -16t^2-12t+52=0 equation: 


Simplifying
-16t2 + -12t + 52 = 0

Reorder the terms:
52 + -12t + -16t2 = 0

Solving
52 + -12t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(13 + -3t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(13 + -3t + -4t2)' equal to zero and attempt to solve:

Simplifying
13 + -3t + -4t2 = 0

Solving
13 + -3t + -4t2 = 0

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

Divide each side by '-4'.
-3.25 + 0.75t + t2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 0.75t + 3.25 + t2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 0.75t + t2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 0.75t + t2 = 0 + 3.25
0.75t + t2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
0.75t + t2 = 3.25

The t term is 0.75t.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75t + 0.140625 + t2 = 3.25 + 0.140625

Reorder the terms:
0.140625 + 0.75t + t2 = 3.25 + 0.140625

Combine like terms: 3.25 + 0.140625 = 3.390625
0.140625 + 0.75t + t2 = 3.390625

Factor a perfect square on the left side:
(t + 0.375)(t + 0.375) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(t + 0.375) equal to 1.841364983 and -1.841364983.


Subproblem 1
t + 0.375 = 1.841364983

Simplifying
t + 0.375 = 1.841364983

Reorder the terms:
0.375 + t = 1.841364983

Solving
0.375 + t = 1.841364983

Solving for variable 't'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + t = 1.841364983 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + t = 1.841364983 + -0.375
t = 1.841364983 + -0.375

Combine like terms: 1.841364983 + -0.375 = 1.466364983
t = 1.466364983

Simplifying
t = 1.466364983


Subproblem 2
t + 0.375 = -1.841364983

Simplifying
t + 0.375 = -1.841364983

Reorder the terms:
0.375 + t = -1.841364983

Solving
0.375 + t = -1.841364983

Solving for variable 't'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + t = -1.841364983 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + t = -1.841364983 + -0.375
t = -1.841364983 + -0.375

Combine like terms: -1.841364983 + -0.375 = -2.216364983
t = -2.216364983

Simplifying
t = -2.216364983


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.466364983, -2.216364983}
Solution
t = {1.466364983, -2.216364983}

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