-16t^2+64t+12=0

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Solution for -16t^2+64t+12=0 equation: 


Simplifying
-16t2 + 64t + 12 = 0

Reorder the terms:
12 + 64t + -16t2 = 0

Solving
12 + 64t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 16t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 16t + -4t2)' equal to zero and attempt to solve:

Simplifying
3 + 16t + -4t2 = 0

Solving
3 + 16t + -4t2 = 0

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

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

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -4t + 0.75 + t2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -4t + t2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -4t + t2 = 0 + 0.75
-4t + t2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-4t + t2 = 0.75

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 0.75 + 4

Reorder the terms:
4 + -4t + t2 = 0.75 + 4

Combine like terms: 0.75 + 4 = 4.75
4 + -4t + t2 = 4.75

Factor a perfect square on the left side:
(t + -2)(t + -2) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(t + -2) equal to 2.179449472 and -2.179449472.


Subproblem 1
t + -2 = 2.179449472

Simplifying
t + -2 = 2.179449472

Reorder the terms:
-2 + t = 2.179449472

Solving
-2 + t = 2.179449472

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 2.179449472 + 2

Combine like terms: -2 + 2 = 0
0 + t = 2.179449472 + 2
t = 2.179449472 + 2

Combine like terms: 2.179449472 + 2 = 4.179449472
t = 4.179449472

Simplifying
t = 4.179449472


Subproblem 2
t + -2 = -2.179449472

Simplifying
t + -2 = -2.179449472

Reorder the terms:
-2 + t = -2.179449472

Solving
-2 + t = -2.179449472

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -2.179449472 + 2

Combine like terms: -2 + 2 = 0
0 + t = -2.179449472 + 2
t = -2.179449472 + 2

Combine like terms: -2.179449472 + 2 = -0.179449472
t = -0.179449472

Simplifying
t = -0.179449472


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.179449472, -0.179449472}
Solution
t = {4.179449472, -0.179449472}

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