132(t)=16t^2+132

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Solution for 132(t)=16t^2+132 equation: 


Simplifying
132(t) = 16t2 + 132

Reorder the terms:
132t = 132 + 16t2

Solving
132t = 132 + 16t2

Solving for variable 't'.

Reorder the terms:
-132 + 132t + -16t2 = 132 + 16t2 + -132 + -16t2

Reorder the terms:
-132 + 132t + -16t2 = 132 + -132 + 16t2 + -16t2

Combine like terms: 132 + -132 = 0
-132 + 132t + -16t2 = 0 + 16t2 + -16t2
-132 + 132t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-132 + 132t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-33 + 33t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-33 + 33t + -4t2)' equal to zero and attempt to solve:

Simplifying
-33 + 33t + -4t2 = 0

Solving
-33 + 33t + -4t2 = 0

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

Divide each side by '-4'.
8.25 + -8.25t + t2 = 0

Move the constant term to the right:

Add '-8.25' to each side of the equation.
8.25 + -8.25t + -8.25 + t2 = 0 + -8.25

Reorder the terms:
8.25 + -8.25 + -8.25t + t2 = 0 + -8.25

Combine like terms: 8.25 + -8.25 = 0.00
0.00 + -8.25t + t2 = 0 + -8.25
-8.25t + t2 = 0 + -8.25

Combine like terms: 0 + -8.25 = -8.25
-8.25t + t2 = -8.25

The t term is -8.25t.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25t + 17.015625 + t2 = -8.25 + 17.015625

Reorder the terms:
17.015625 + -8.25t + t2 = -8.25 + 17.015625

Combine like terms: -8.25 + 17.015625 = 8.765625
17.015625 + -8.25t + t2 = 8.765625

Factor a perfect square on the left side:
(t + -4.125)(t + -4.125) = 8.765625

Calculate the square root of the right side: 2.960679821

Break this problem into two subproblems by setting 
(t + -4.125) equal to 2.960679821 and -2.960679821.


Subproblem 1
t + -4.125 = 2.960679821

Simplifying
t + -4.125 = 2.960679821

Reorder the terms:
-4.125 + t = 2.960679821

Solving
-4.125 + t = 2.960679821

Solving for variable 't'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + t = 2.960679821 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + t = 2.960679821 + 4.125
t = 2.960679821 + 4.125

Combine like terms: 2.960679821 + 4.125 = 7.085679821
t = 7.085679821

Simplifying
t = 7.085679821


Subproblem 2
t + -4.125 = -2.960679821

Simplifying
t + -4.125 = -2.960679821

Reorder the terms:
-4.125 + t = -2.960679821

Solving
-4.125 + t = -2.960679821

Solving for variable 't'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + t = -2.960679821 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + t = -2.960679821 + 4.125
t = -2.960679821 + 4.125

Combine like terms: -2.960679821 + 4.125 = 1.164320179
t = 1.164320179

Simplifying
t = 1.164320179


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.085679821, 1.164320179}
Solution
t = {7.085679821, 1.164320179}

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