2[(x-4)(x-4)]=26

Solution for 2[(x-4)(x-4)]=26 equation:

Simplifying
2[(x + -4)(x + -4)] = 26

Reorder the terms:
2[(-4 + x)(x + -4)] = 26

Reorder the terms:
2[(-4 + x)(-4 + x)] = 26

Multiply (-4 + x) * (-4 + x)
2[(-4(-4 + x) + x(-4 + x))] = 26
2[((-4 * -4 + x * -4) + x(-4 + x))] = 26
2[((16 + -4x) + x(-4 + x))] = 26
2[(16 + -4x + (-4 * x + x * x))] = 26
2[(16 + -4x + (-4x + x2))] = 26

Combine like terms: -4x + -4x = -8x
2[(16 + -8x + x2)] = 26
[16 * 2 + -8x * 2 + x2 * 2] = 26
[32 + -16x + 2x2] = 26

Solving
32 + -16x + 2x2 = 26

Solving for variable 'x'.

Reorder the terms:
32 + -26 + -16x + 2x2 = 26 + -26

Combine like terms: 32 + -26 = 6
6 + -16x + 2x2 = 26 + -26

Combine like terms: 26 + -26 = 0
6 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -8x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
3 + -8x + x2 = 0

Solving
3 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -8x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -8x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x + x2 = 0 + -3
-8x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8x + x2 = -3

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -3 + 16

Reorder the terms:
16 + -8x + x2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + -8x + x2 = 13

Factor a perfect square on the left side:
(x + -4)(x + -4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -4) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + -4 = 3.605551275

Simplifying
x + -4 = 3.605551275

Reorder the terms:
-4 + x = 3.605551275

Solving
-4 + x = 3.605551275

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.605551275 + 4
x = 3.605551275 + 4

Combine like terms: 3.605551275 + 4 = 7.605551275
x = 7.605551275

Simplifying
x = 7.605551275

Subproblem 2
x + -4 = -3.605551275

Simplifying
x + -4 = -3.605551275

Reorder the terms:
-4 + x = -3.605551275

Solving
-4 + x = -3.605551275

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.605551275 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.605551275 + 4
x = -3.605551275 + 4

Combine like terms: -3.605551275 + 4 = 0.394448725
x = 0.394448725

Simplifying
x = 0.394448725

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.605551275, 0.394448725}
Solution
x = {7.605551275, 0.394448725}