0=64+64t-16t^2

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


Simplifying
0 = 64 + 64t + -16t2

Solving
0 = 64 + 64t + -16t2

Solving for variable 't'.

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

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

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

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

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

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

Ignore the factor 16.

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

Simplifying
-4 + -4t + t2 = 0

Solving
-4 + -4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + -4t + t2 = 8

Factor a perfect square on the left side:
(t + -2)(t + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(t + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
t + -2 = 2.828427125

Simplifying
t + -2 = 2.828427125

Reorder the terms:
-2 + t = 2.828427125

Solving
-2 + t = 2.828427125

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 = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + t = 2.828427125 + 2
t = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
t = 4.828427125

Simplifying
t = 4.828427125


Subproblem 2
t + -2 = -2.828427125

Simplifying
t + -2 = -2.828427125

Reorder the terms:
-2 + t = -2.828427125

Solving
-2 + t = -2.828427125

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 = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + t = -2.828427125 + 2
t = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
t = -0.828427125

Simplifying
t = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.828427125, -0.828427125}
Solution
t = {4.828427125, -0.828427125}

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