x=(0.250+x)*(0.250+x)

Solution for x=(0.250+x)*(0.250+x) equation:

Simplifying
x = (0.250 + x)(0.250 + x)

Multiply (0.250 + x) * (0.250 + x)
x = (0.250(0.250 + x) + x(0.250 + x))
x = ((0.250 * 0.250 + x * 0.250) + x(0.250 + x))
x = ((0.0625 + 0.250x) + x(0.250 + x))
x = (0.0625 + 0.250x + (0.250 * x + x * x))
x = (0.0625 + 0.250x + (0.250x + x2))

Combine like terms: 0.250x + 0.250x = 0.5x
x = (0.0625 + 0.5x + x2)

Solving
x = 0.0625 + 0.5x + x2

Solving for variable 'x'.

Reorder the terms:
-0.0625 + x + -0.5x + -1x2 = 0.0625 + 0.5x + x2 + -0.0625 + -0.5x + -1x2

Combine like terms: x + -0.5x = 0.5x
-0.0625 + 0.5x + -1x2 = 0.0625 + 0.5x + x2 + -0.0625 + -0.5x + -1x2

Reorder the terms:
-0.0625 + 0.5x + -1x2 = 0.0625 + -0.0625 + 0.5x + -0.5x + x2 + -1x2

Combine like terms: 0.0625 + -0.0625 = 0.0000
-0.0625 + 0.5x + -1x2 = 0.0000 + 0.5x + -0.5x + x2 + -1x2
-0.0625 + 0.5x + -1x2 = 0.5x + -0.5x + x2 + -1x2

Combine like terms: 0.5x + -0.5x = 0.0
-0.0625 + 0.5x + -1x2 = 0.0 + x2 + -1x2
-0.0625 + 0.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-0.0625 + 0.5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.0625 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -0.5x + -0.0625 + x2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -0.5x + x2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -0.5x + x2 = 0 + -0.0625
-0.5x + x2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-0.5x + x2 = -0.0625

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.0625 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.0625 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0625 + -0.5x + x2 = 0.0000

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.0000

Calculate the square root of the right side: 0.0000

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.0000 and 0.0000.

Subproblem 1
x + -0.25 = 0.0000

Simplifying
x + -0.25 = 0.0000

Reorder the terms:
-0.25 + x = 0.0000

Solving
-0.25 + x = 0.0000

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.0000 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.0000 + 0.25
x = 0.0000 + 0.25

Combine like terms: 0.0000 + 0.25 = 0.25
x = 0.25

Simplifying
x = 0.25

Subproblem 2
x + -0.25 = 0.0000

Simplifying
x + -0.25 = 0.0000

Reorder the terms:
-0.25 + x = 0.0000

Solving
-0.25 + x = 0.0000

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.0000 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.0000 + 0.25
x = 0.0000 + 0.25

Combine like terms: 0.0000 + 0.25 = 0.25
x = 0.25

Simplifying
x = 0.25

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.25, 0.25}