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

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

Simplifying
x2 = (1 + -2x)(1 + -2x) * 0.45

Reorder the terms for easier multiplication:
x2 = 0.45(1 + -2x)(1 + -2x)

Multiply (1 + -2x) * (1 + -2x)
x2 = 0.45(1(1 + -2x) + -2x * (1 + -2x))
x2 = 0.45((1 * 1 + -2x * 1) + -2x * (1 + -2x))
x2 = 0.45((1 + -2x) + -2x * (1 + -2x))
x2 = 0.45(1 + -2x + (1 * -2x + -2x * -2x))
x2 = 0.45(1 + -2x + (-2x + 4x2))

Combine like terms: -2x + -2x = -4x
x2 = 0.45(1 + -4x + 4x2)
x2 = (1 * 0.45 + -4x * 0.45 + 4x2 * 0.45)
x2 = (0.45 + -1.8x + 1.8x2)

Solving
x2 = 0.45 + -1.8x + 1.8x2

Solving for variable 'x'.

Reorder the terms:
-0.45 + 1.8x + x2 + -1.8x2 = 0.45 + -1.8x + 1.8x2 + -0.45 + 1.8x + -1.8x2

Combine like terms: x2 + -1.8x2 = -0.8x2
-0.45 + 1.8x + -0.8x2 = 0.45 + -1.8x + 1.8x2 + -0.45 + 1.8x + -1.8x2

Reorder the terms:
-0.45 + 1.8x + -0.8x2 = 0.45 + -0.45 + -1.8x + 1.8x + 1.8x2 + -1.8x2

Combine like terms: 0.45 + -0.45 = 0.00
-0.45 + 1.8x + -0.8x2 = 0.00 + -1.8x + 1.8x + 1.8x2 + -1.8x2
-0.45 + 1.8x + -0.8x2 = -1.8x + 1.8x + 1.8x2 + -1.8x2

Combine like terms: -1.8x + 1.8x = 0.0
-0.45 + 1.8x + -0.8x2 = 0.0 + 1.8x2 + -1.8x2
-0.45 + 1.8x + -0.8x2 = 1.8x2 + -1.8x2

Combine like terms: 1.8x2 + -1.8x2 = 0.0
-0.45 + 1.8x + -0.8x2 = 0.0

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
0.5625 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-0.5625' to each side of the equation.
0.5625 + -2.25x + -0.5625 + x2 = 0 + -0.5625

Reorder the terms:
0.5625 + -0.5625 + -2.25x + x2 = 0 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + -2.25x + x2 = 0 + -0.5625
-2.25x + x2 = 0 + -0.5625

Combine like terms: 0 + -0.5625 = -0.5625
-2.25x + x2 = -0.5625

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -0.5625 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -0.5625 + 1.265625

Combine like terms: -0.5625 + 1.265625 = 0.703125
1.265625 + -2.25x + x2 = 0.703125

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.703125

Calculate the square root of the right side: 0.838525492

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.838525492 and -0.838525492.

Subproblem 1
x + -1.125 = 0.838525492

Simplifying
x + -1.125 = 0.838525492

Reorder the terms:
-1.125 + x = 0.838525492

Solving
-1.125 + x = 0.838525492

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 0.838525492 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 0.838525492 + 1.125
x = 0.838525492 + 1.125

Combine like terms: 0.838525492 + 1.125 = 1.963525492
x = 1.963525492

Simplifying
x = 1.963525492

Subproblem 2
x + -1.125 = -0.838525492

Simplifying
x + -1.125 = -0.838525492

Reorder the terms:
-1.125 + x = -0.838525492

Solving
-1.125 + x = -0.838525492

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -0.838525492 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -0.838525492 + 1.125
x = -0.838525492 + 1.125

Combine like terms: -0.838525492 + 1.125 = 0.286474508
x = 0.286474508

Simplifying
x = 0.286474508

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.963525492, 0.286474508}