2-3*(x-1)*(x-1)=0

Solution for 2-3*(x-1)*(x-1)=0 equation:

Simplifying
2 + -3(x + -1)(x + -1) = 0

Reorder the terms:
2 + -3(-1 + x)(x + -1) = 0

Reorder the terms:
2 + -3(-1 + x)(-1 + x) = 0

Multiply (-1 + x) * (-1 + x)
2 + -3(-1(-1 + x) + x(-1 + x)) = 0
2 + -3((-1 * -1 + x * -1) + x(-1 + x)) = 0
2 + -3((1 + -1x) + x(-1 + x)) = 0
2 + -3(1 + -1x + (-1 * x + x * x)) = 0
2 + -3(1 + -1x + (-1x + x2)) = 0

Combine like terms: -1x + -1x = -2x
2 + -3(1 + -2x + x2) = 0
2 + (1 * -3 + -2x * -3 + x2 * -3) = 0
2 + (-3 + 6x + -3x2) = 0

Combine like terms: 2 + -3 = -1
-1 + 6x + -3x2 = 0

Solving
-1 + 6x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
0.3333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -2x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -2x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.3333333333
-2x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-2x + x2 = -0.3333333333

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 = -0.3333333333 + 1

Reorder the terms:
1 + -2x + x2 = -0.3333333333 + 1

Combine like terms: -0.3333333333 + 1 = 0.6666666667
1 + -2x + x2 = 0.6666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.6666666667

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + -1) equal to 0.816496581 and -0.816496581.

Subproblem 1
x + -1 = 0.816496581

Simplifying
x + -1 = 0.816496581

Reorder the terms:
-1 + x = 0.816496581

Solving
-1 + x = 0.816496581

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 = 0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.816496581 + 1
x = 0.816496581 + 1

Combine like terms: 0.816496581 + 1 = 1.816496581
x = 1.816496581

Simplifying
x = 1.816496581

Subproblem 2
x + -1 = -0.816496581

Simplifying
x + -1 = -0.816496581

Reorder the terms:
-1 + x = -0.816496581

Solving
-1 + x = -0.816496581

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 = -0.816496581 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.816496581 + 1
x = -0.816496581 + 1

Combine like terms: -0.816496581 + 1 = 0.183503419
x = 0.183503419

Simplifying
x = 0.183503419

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.816496581, 0.183503419}