2(u^2+4u+4)=64

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Solution for 2(u^2+4u+4)=64 equation: 


Simplifying
2(u2 + 4u + 4) = 64

Reorder the terms:
2(4 + 4u + u2) = 64
(4 * 2 + 4u * 2 + u2 * 2) = 64
(8 + 8u + 2u2) = 64

Solving
8 + 8u + 2u2 = 64

Solving for variable 'u'.

Reorder the terms:
8 + -64 + 8u + 2u2 = 64 + -64

Combine like terms: 8 + -64 = -56
-56 + 8u + 2u2 = 64 + -64

Combine like terms: 64 + -64 = 0
-56 + 8u + 2u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 4u + u2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-28 + 4u + u2)' equal to zero and attempt to solve:

Simplifying
-28 + 4u + u2 = 0

Solving
-28 + 4u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 4u + 28 + u2 = 0 + 28

Reorder the terms:
-28 + 28 + 4u + u2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 4u + u2 = 0 + 28
4u + u2 = 0 + 28

Combine like terms: 0 + 28 = 28
4u + u2 = 28

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

Add '4' to each side of the equation.
4u + 4 + u2 = 28 + 4

Reorder the terms:
4 + 4u + u2 = 28 + 4

Combine like terms: 28 + 4 = 32
4 + 4u + u2 = 32

Factor a perfect square on the left side:
(u + 2)(u + 2) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(u + 2) equal to 5.656854249 and -5.656854249.


Subproblem 1
u + 2 = 5.656854249

Simplifying
u + 2 = 5.656854249

Reorder the terms:
2 + u = 5.656854249

Solving
2 + u = 5.656854249

Solving for variable 'u'.

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

Add '-2' to each side of the equation.
2 + -2 + u = 5.656854249 + -2

Combine like terms: 2 + -2 = 0
0 + u = 5.656854249 + -2
u = 5.656854249 + -2

Combine like terms: 5.656854249 + -2 = 3.656854249
u = 3.656854249

Simplifying
u = 3.656854249


Subproblem 2
u + 2 = -5.656854249

Simplifying
u + 2 = -5.656854249

Reorder the terms:
2 + u = -5.656854249

Solving
2 + u = -5.656854249

Solving for variable 'u'.

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

Add '-2' to each side of the equation.
2 + -2 + u = -5.656854249 + -2

Combine like terms: 2 + -2 = 0
0 + u = -5.656854249 + -2
u = -5.656854249 + -2

Combine like terms: -5.656854249 + -2 = -7.656854249
u = -7.656854249

Simplifying
u = -7.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.656854249, -7.656854249}
Solution
u = {3.656854249, -7.656854249}

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