x^2+(x^2+8x+16)=64

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Solution for x^2+(x^2+8x+16)=64 equation: 


Simplifying
x2 + (x2 + 8x + 16) = 64

Reorder the terms:
x2 + (16 + 8x + x2) = 64

Remove parenthesis around (16 + 8x + x2)
x2 + 16 + 8x + x2 = 64

Reorder the terms:
16 + 8x + x2 + x2 = 64

Combine like terms: x2 + x2 = 2x2
16 + 8x + 2x2 = 64

Solving
16 + 8x + 2x2 = 64

Solving for variable 'x'.

Reorder the terms:
16 + -64 + 8x + 2x2 = 64 + -64

Combine like terms: 16 + -64 = -48
-48 + 8x + 2x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-48 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 4x + x2 = 0

Solving
-24 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 4x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 4x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 4x + x2 = 0 + 24
4x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
4x + x2 = 24

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

Add '4' to each side of the equation.
4x + 4 + x2 = 24 + 4

Reorder the terms:
4 + 4x + x2 = 24 + 4

Combine like terms: 24 + 4 = 28
4 + 4x + x2 = 28

Factor a perfect square on the left side:
(x + 2)(x + 2) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + 2) equal to 5.291502622 and -5.291502622.


Subproblem 1
x + 2 = 5.291502622

Simplifying
x + 2 = 5.291502622

Reorder the terms:
2 + x = 5.291502622

Solving
2 + x = 5.291502622

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 5.291502622 + -2

Combine like terms: 2 + -2 = 0
0 + x = 5.291502622 + -2
x = 5.291502622 + -2

Combine like terms: 5.291502622 + -2 = 3.291502622
x = 3.291502622

Simplifying
x = 3.291502622


Subproblem 2
x + 2 = -5.291502622

Simplifying
x + 2 = -5.291502622

Reorder the terms:
2 + x = -5.291502622

Solving
2 + x = -5.291502622

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -5.291502622 + -2

Combine like terms: 2 + -2 = 0
0 + x = -5.291502622 + -2
x = -5.291502622 + -2

Combine like terms: -5.291502622 + -2 = -7.291502622
x = -7.291502622

Simplifying
x = -7.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.291502622, -7.291502622}
Solution
x = {3.291502622, -7.291502622}

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