(x+16)(x+16)=2

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Solution for (x+16)(x+16)=2 equation: 


Simplifying
(x + 16)(x + 16) = 2

Reorder the terms:
(16 + x)(x + 16) = 2

Reorder the terms:
(16 + x)(16 + x) = 2

Multiply (16 + x) * (16 + x)
(16(16 + x) + x(16 + x)) = 2
((16 * 16 + x * 16) + x(16 + x)) = 2
((256 + 16x) + x(16 + x)) = 2
(256 + 16x + (16 * x + x * x)) = 2
(256 + 16x + (16x + x2)) = 2

Combine like terms: 16x + 16x = 32x
(256 + 32x + x2) = 2

Solving
256 + 32x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
256 + -2 + 32x + x2 = 2 + -2

Combine like terms: 256 + -2 = 254
254 + 32x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
254 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-254' to each side of the equation.
254 + 32x + -254 + x2 = 0 + -254

Reorder the terms:
254 + -254 + 32x + x2 = 0 + -254

Combine like terms: 254 + -254 = 0
0 + 32x + x2 = 0 + -254
32x + x2 = 0 + -254

Combine like terms: 0 + -254 = -254
32x + x2 = -254

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = -254 + 256

Reorder the terms:
256 + 32x + x2 = -254 + 256

Combine like terms: -254 + 256 = 2
256 + 32x + x2 = 2

Factor a perfect square on the left side:
(x + 16)(x + 16) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 16) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + 16 = 1.414213562

Simplifying
x + 16 = 1.414213562

Reorder the terms:
16 + x = 1.414213562

Solving
16 + x = 1.414213562

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = 1.414213562 + -16

Combine like terms: 16 + -16 = 0
0 + x = 1.414213562 + -16
x = 1.414213562 + -16

Combine like terms: 1.414213562 + -16 = -14.585786438
x = -14.585786438

Simplifying
x = -14.585786438


Subproblem 2
x + 16 = -1.414213562

Simplifying
x + 16 = -1.414213562

Reorder the terms:
16 + x = -1.414213562

Solving
16 + x = -1.414213562

Solving for variable 'x'.

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

Add '-16' to each side of the equation.
16 + -16 + x = -1.414213562 + -16

Combine like terms: 16 + -16 = 0
0 + x = -1.414213562 + -16
x = -1.414213562 + -16

Combine like terms: -1.414213562 + -16 = -17.414213562
x = -17.414213562

Simplifying
x = -17.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-14.585786438, -17.414213562}

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