14=2+36t-16t^2

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Solution for 14=2+36t-16t^2 equation: 


Simplifying
14 = 2 + 36t + -16t2

Solving
14 = 2 + 36t + -16t2

Solving for variable 't'.

Combine like terms: 14 + -2 = 12
12 + -36t + 16t2 = 2 + 36t + -16t2 + -2 + -36t + 16t2

Reorder the terms:
12 + -36t + 16t2 = 2 + -2 + 36t + -36t + -16t2 + 16t2

Combine like terms: 2 + -2 = 0
12 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2
12 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2

Combine like terms: 36t + -36t = 0
12 + -36t + 16t2 = 0 + -16t2 + 16t2
12 + -36t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
12 + -36t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -9t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + -9t + 4t2)' equal to zero and attempt to solve:

Simplifying
3 + -9t + 4t2 = 0

Solving
3 + -9t + 4t2 = 0

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

Divide each side by '4'.
0.75 + -2.25t + t2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -2.25t + -0.75 + t2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -2.25t + t2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -2.25t + t2 = 0 + -0.75
-2.25t + t2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-2.25t + t2 = -0.75

The t term is -2.25t.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25t + 1.265625 + t2 = -0.75 + 1.265625

Reorder the terms:
1.265625 + -2.25t + t2 = -0.75 + 1.265625

Combine like terms: -0.75 + 1.265625 = 0.515625
1.265625 + -2.25t + t2 = 0.515625

Factor a perfect square on the left side:
(t + -1.125)(t + -1.125) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(t + -1.125) equal to 0.718070331 and -0.718070331.


Subproblem 1
t + -1.125 = 0.718070331

Simplifying
t + -1.125 = 0.718070331

Reorder the terms:
-1.125 + t = 0.718070331

Solving
-1.125 + t = 0.718070331

Solving for variable 't'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + t = 0.718070331 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + t = 0.718070331 + 1.125
t = 0.718070331 + 1.125

Combine like terms: 0.718070331 + 1.125 = 1.843070331
t = 1.843070331

Simplifying
t = 1.843070331


Subproblem 2
t + -1.125 = -0.718070331

Simplifying
t + -1.125 = -0.718070331

Reorder the terms:
-1.125 + t = -0.718070331

Solving
-1.125 + t = -0.718070331

Solving for variable 't'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + t = -0.718070331 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + t = -0.718070331 + 1.125
t = -0.718070331 + 1.125

Combine like terms: -0.718070331 + 1.125 = 0.406929669
t = 0.406929669

Simplifying
t = 0.406929669


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.843070331, 0.406929669}
Solution
t = {1.843070331, 0.406929669}

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