2(x-1)(x-1)-36=0

Solution for 2(x-1)(x-1)-36=0 equation:

Simplifying
2(x + -1)(x + -1) + -36 = 0

Reorder the terms:
2(-1 + x)(x + -1) + -36 = 0

Reorder the terms:
2(-1 + x)(-1 + x) + -36 = 0

Multiply (-1 + x) * (-1 + x)
2(-1(-1 + x) + x(-1 + x)) + -36 = 0
2((-1 * -1 + x * -1) + x(-1 + x)) + -36 = 0
2((1 + -1x) + x(-1 + x)) + -36 = 0
2(1 + -1x + (-1 * x + x * x)) + -36 = 0
2(1 + -1x + (-1x + x2)) + -36 = 0

Combine like terms: -1x + -1x = -2x
2(1 + -2x + x2) + -36 = 0
(1 * 2 + -2x * 2 + x2 * 2) + -36 = 0
(2 + -4x + 2x2) + -36 = 0

Reorder the terms:
2 + -36 + -4x + 2x2 = 0

Combine like terms: 2 + -36 = -34
-34 + -4x + 2x2 = 0

Solving
-34 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + -2x + x2 = 0

Solving
-17 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -2x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -2x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2x + x2 = 0 + 17
-2x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-2x + x2 = 17

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 = 17 + 1

Reorder the terms:
1 + -2x + x2 = 17 + 1

Combine like terms: 17 + 1 = 18
1 + -2x + x2 = 18

Factor a perfect square on the left side:
(x + -1)(x + -1) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -1) equal to 4.242640687 and -4.242640687.

Subproblem 1
x + -1 = 4.242640687

Simplifying
x + -1 = 4.242640687

Reorder the terms:
-1 + x = 4.242640687

Solving
-1 + x = 4.242640687

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 = 4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.242640687 + 1
x = 4.242640687 + 1

Combine like terms: 4.242640687 + 1 = 5.242640687
x = 5.242640687

Simplifying
x = 5.242640687

Subproblem 2
x + -1 = -4.242640687

Simplifying
x + -1 = -4.242640687

Reorder the terms:
-1 + x = -4.242640687

Solving
-1 + x = -4.242640687

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 = -4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.242640687 + 1
x = -4.242640687 + 1

Combine like terms: -4.242640687 + 1 = -3.242640687
x = -3.242640687

Simplifying
x = -3.242640687

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.242640687, -3.242640687}
Solution
x = {5.242640687, -3.242640687}