32=16t^2+64t+4

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Solution for 32=16t^2+64t+4 equation: 


Simplifying
32 = 16t2 + 64t + 4

Reorder the terms:
32 = 4 + 64t + 16t2

Solving
32 = 4 + 64t + 16t2

Solving for variable 't'.

Combine like terms: 32 + -4 = 28
28 + -64t + -16t2 = 4 + 64t + 16t2 + -4 + -64t + -16t2

Reorder the terms:
28 + -64t + -16t2 = 4 + -4 + 64t + -64t + 16t2 + -16t2

Combine like terms: 4 + -4 = 0
28 + -64t + -16t2 = 0 + 64t + -64t + 16t2 + -16t2
28 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2

Combine like terms: 64t + -64t = 0
28 + -64t + -16t2 = 0 + 16t2 + -16t2
28 + -64t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
28 + -64t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -16t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + -16t + -4t2)' equal to zero and attempt to solve:

Simplifying
7 + -16t + -4t2 = 0

Solving
7 + -16t + -4t2 = 0

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

Divide each side by '-4'.
-1.75 + 4t + t2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 4t + 1.75 + t2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 4t + t2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 4t + t2 = 0 + 1.75
4t + t2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
4t + t2 = 1.75

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 = 1.75 + 4

Reorder the terms:
4 + 4t + t2 = 1.75 + 4

Combine like terms: 1.75 + 4 = 5.75
4 + 4t + t2 = 5.75

Factor a perfect square on the left side:
(t + 2)(t + 2) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(t + 2) equal to 2.397915762 and -2.397915762.


Subproblem 1
t + 2 = 2.397915762

Simplifying
t + 2 = 2.397915762

Reorder the terms:
2 + t = 2.397915762

Solving
2 + t = 2.397915762

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 = 2.397915762 + -2

Combine like terms: 2 + -2 = 0
0 + t = 2.397915762 + -2
t = 2.397915762 + -2

Combine like terms: 2.397915762 + -2 = 0.397915762
t = 0.397915762

Simplifying
t = 0.397915762


Subproblem 2
t + 2 = -2.397915762

Simplifying
t + 2 = -2.397915762

Reorder the terms:
2 + t = -2.397915762

Solving
2 + t = -2.397915762

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 = -2.397915762 + -2

Combine like terms: 2 + -2 = 0
0 + t = -2.397915762 + -2
t = -2.397915762 + -2

Combine like terms: -2.397915762 + -2 = -4.397915762
t = -4.397915762

Simplifying
t = -4.397915762


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.397915762, -4.397915762}
Solution
t = {0.397915762, -4.397915762}

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