2(x-1)(x-1)=3

Solution for 2(x-1)(x-1)=3 equation:

Simplifying
2(x + -1)(x + -1) = 3

Reorder the terms:
2(-1 + x)(x + -1) = 3

Reorder the terms:
2(-1 + x)(-1 + x) = 3

Multiply (-1 + x) * (-1 + x)
2(-1(-1 + x) + x(-1 + x)) = 3
2((-1 * -1 + x * -1) + x(-1 + x)) = 3
2((1 + -1x) + x(-1 + x)) = 3
2(1 + -1x + (-1 * x + x * x)) = 3
2(1 + -1x + (-1x + x2)) = 3

Combine like terms: -1x + -1x = -2x
2(1 + -2x + x2) = 3
(1 * 2 + -2x * 2 + x2 * 2) = 3
(2 + -4x + 2x2) = 3

Solving
2 + -4x + 2x2 = 3

Solving for variable 'x'.

Reorder the terms:
2 + -3 + -4x + 2x2 = 3 + -3

Combine like terms: 2 + -3 = -1
-1 + -4x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-1 + -4x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + -2x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -2x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -2x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -2x + x2 = 0 + 0.5
-2x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-2x + x2 = 0.5

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 = 0.5 + 1

Reorder the terms:
1 + -2x + x2 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + -2x + x2 = 1.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + -1) equal to 1.224744871 and -1.224744871.

Subproblem 1
x + -1 = 1.224744871

Simplifying
x + -1 = 1.224744871

Reorder the terms:
-1 + x = 1.224744871

Solving
-1 + x = 1.224744871

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 = 1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.224744871 + 1
x = 1.224744871 + 1

Combine like terms: 1.224744871 + 1 = 2.224744871
x = 2.224744871

Simplifying
x = 2.224744871

Subproblem 2
x + -1 = -1.224744871

Simplifying
x + -1 = -1.224744871

Reorder the terms:
-1 + x = -1.224744871

Solving
-1 + x = -1.224744871

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 = -1.224744871 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.224744871 + 1
x = -1.224744871 + 1

Combine like terms: -1.224744871 + 1 = -0.224744871
x = -0.224744871

Simplifying
x = -0.224744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.224744871, -0.224744871}