x^2=(1-x)*(1-x)*0.45

Solution for x^2=(1-x)*(1-x)*0.45 equation:

Simplifying
x2 = (1 + -1x)(1 + -1x) * 0.45

Reorder the terms for easier multiplication:
x2 = 0.45(1 + -1x)(1 + -1x)

Multiply (1 + -1x) * (1 + -1x)
x2 = 0.45(1(1 + -1x) + -1x * (1 + -1x))
x2 = 0.45((1 * 1 + -1x * 1) + -1x * (1 + -1x))
x2 = 0.45((1 + -1x) + -1x * (1 + -1x))
x2 = 0.45(1 + -1x + (1 * -1x + -1x * -1x))
x2 = 0.45(1 + -1x + (-1x + 1x2))

Combine like terms: -1x + -1x = -2x
x2 = 0.45(1 + -2x + 1x2)
x2 = (1 * 0.45 + -2x * 0.45 + 1x2 * 0.45)
x2 = (0.45 + -0.9x + 0.45x2)

Solving
x2 = 0.45 + -0.9x + 0.45x2

Solving for variable 'x'.

Reorder the terms:
-0.45 + 0.9x + x2 + -0.45x2 = 0.45 + -0.9x + 0.45x2 + -0.45 + 0.9x + -0.45x2

Combine like terms: x2 + -0.45x2 = 0.55x2
-0.45 + 0.9x + 0.55x2 = 0.45 + -0.9x + 0.45x2 + -0.45 + 0.9x + -0.45x2

Reorder the terms:
-0.45 + 0.9x + 0.55x2 = 0.45 + -0.45 + -0.9x + 0.9x + 0.45x2 + -0.45x2

Combine like terms: 0.45 + -0.45 = 0.00
-0.45 + 0.9x + 0.55x2 = 0.00 + -0.9x + 0.9x + 0.45x2 + -0.45x2
-0.45 + 0.9x + 0.55x2 = -0.9x + 0.9x + 0.45x2 + -0.45x2

Combine like terms: -0.9x + 0.9x = 0.0
-0.45 + 0.9x + 0.55x2 = 0.0 + 0.45x2 + -0.45x2
-0.45 + 0.9x + 0.55x2 = 0.45x2 + -0.45x2

Combine like terms: 0.45x2 + -0.45x2 = 0.00
-0.45 + 0.9x + 0.55x2 = 0.00

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

Divide each side by '0.55'.
-0.8181818182 + 1.636363636x + x2 = 0

Move the constant term to the right:

Add '0.8181818182' to each side of the equation.
-0.8181818182 + 1.636363636x + 0.8181818182 + x2 = 0 + 0.8181818182

Reorder the terms:
-0.8181818182 + 0.8181818182 + 1.636363636x + x2 = 0 + 0.8181818182

Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000
0.0000000000 + 1.636363636x + x2 = 0 + 0.8181818182
1.636363636x + x2 = 0 + 0.8181818182

Combine like terms: 0 + 0.8181818182 = 0.8181818182
1.636363636x + x2 = 0.8181818182

The x term is 1.636363636x.  Take half its coefficient (0.818181818).
Square it (0.6694214873) and add it to both sides.

Add '0.6694214873' to each side of the equation.
1.636363636x + 0.6694214873 + x2 = 0.8181818182 + 0.6694214873

Reorder the terms:
0.6694214873 + 1.636363636x + x2 = 0.8181818182 + 0.6694214873

Combine like terms: 0.8181818182 + 0.6694214873 = 1.4876033055
0.6694214873 + 1.636363636x + x2 = 1.4876033055

Factor a perfect square on the left side:
(x + 0.818181818)(x + 0.818181818) = 1.4876033055

Calculate the square root of the right side: 1.219673442

Break this problem into two subproblems by setting 
(x + 0.818181818) equal to 1.219673442 and -1.219673442.

Subproblem 1
x + 0.818181818 = 1.219673442

Simplifying
x + 0.818181818 = 1.219673442

Reorder the terms:
0.818181818 + x = 1.219673442

Solving
0.818181818 + x = 1.219673442

Solving for variable 'x'.

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

Add '-0.818181818' to each side of the equation.
0.818181818 + -0.818181818 + x = 1.219673442 + -0.818181818

Combine like terms: 0.818181818 + -0.818181818 = 0.000000000
0.000000000 + x = 1.219673442 + -0.818181818
x = 1.219673442 + -0.818181818

Combine like terms: 1.219673442 + -0.818181818 = 0.401491624
x = 0.401491624

Simplifying
x = 0.401491624

Subproblem 2
x + 0.818181818 = -1.219673442

Simplifying
x + 0.818181818 = -1.219673442

Reorder the terms:
0.818181818 + x = -1.219673442

Solving
0.818181818 + x = -1.219673442

Solving for variable 'x'.

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

Add '-0.818181818' to each side of the equation.
0.818181818 + -0.818181818 + x = -1.219673442 + -0.818181818

Combine like terms: 0.818181818 + -0.818181818 = 0.000000000
0.000000000 + x = -1.219673442 + -0.818181818
x = -1.219673442 + -0.818181818

Combine like terms: -1.219673442 + -0.818181818 = -2.03785526
x = -2.03785526

Simplifying
x = -2.03785526

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.401491624, -2.03785526}