X^2=16+((X-4)+(X+4))

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Solution for X^2=16+((X-4)+(X+4)) equation: 


Simplifying
X2 = 16 + ((X + -4) + (X + 4))

Reorder the terms:
X2 = 16 + ((-4 + X) + (X + 4))

Remove parenthesis around (-4 + X)
X2 = 16 + (-4 + X + (X + 4))

Reorder the terms:
X2 = 16 + (-4 + X + (4 + X))

Remove parenthesis around (4 + X)
X2 = 16 + (-4 + X + 4 + X)

Reorder the terms:
X2 = 16 + (-4 + 4 + X + X)

Combine like terms: -4 + 4 = 0
X2 = 16 + (0 + X + X)
X2 = 16 + (X + X)

Combine like terms: X + X = 2X
X2 = 16 + (2X)
X2 = 16 + (2X)

Solving
X2 = 16 + (2X)

Solving for variable 'X'.

Reorder the terms:
-16 + (-2X) + X2 = 16 + (2X) + -16 + (-2X)

Reorder the terms:
-16 + (-2X) + X2 = 16 + -16 + (2X) + (-2X)

Combine like terms: 16 + -16 = 0
-16 + (-2X) + X2 = 0 + (2X) + (-2X)
-16 + (-2X) + X2 = (2X) + (-2X)

Combine like terms: (2X) + (-2X) = 0
-16 + (-2X) + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + (-2X) + 16 + X2 = 0 + 16

Reorder the terms:
-16 + 16 + (-2X) + X2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + (-2X) + X2 = 0 + 16
(-2X) + X2 = 0 + 16

Combine like terms: 0 + 16 = 16
(-2X) + X2 = 16

The X term is (-2X).  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
(-2X) + 1 + X2 = 16 + 1

Reorder the terms:
1 + (-2X) + X2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + (-2X) + X2 = 17

Factor a perfect square on the left side:
(X + -1)(X + -1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(X + -1) equal to 4.123105626 and -4.123105626.


Subproblem 1
X + -1 = 4.123105626

Simplifying
X + -1 = 4.123105626

Reorder the terms:
-1 + X = 4.123105626

Solving
-1 + X = 4.123105626

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X = 4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + X = 4.123105626 + 1
X = 4.123105626 + 1

Combine like terms: 4.123105626 + 1 = 5.123105626
X = 5.123105626

Simplifying
X = 5.123105626


Subproblem 2
X + -1 = -4.123105626

Simplifying
X + -1 = -4.123105626

Reorder the terms:
-1 + X = -4.123105626

Solving
-1 + X = -4.123105626

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X = -4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + X = -4.123105626 + 1
X = -4.123105626 + 1

Combine like terms: -4.123105626 + 1 = -3.123105626
X = -3.123105626

Simplifying
X = -3.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {5.123105626, -3.123105626}

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