0.17(0.5-x)=(0.1+x)(0.1+x)

Solution for 0.17(0.5-x)=(0.1+x)(0.1+x) equation:

Simplifying
0.17(0.5 + -1x) = (0.1 + x)(0.1 + x)
(0.5 * 0.17 + -1x * 0.17) = (0.1 + x)(0.1 + x)
(0.085 + -0.17x) = (0.1 + x)(0.1 + x)

Multiply (0.1 + x) * (0.1 + x)
0.085 + -0.17x = (0.1(0.1 + x) + x(0.1 + x))
0.085 + -0.17x = ((0.1 * 0.1 + x * 0.1) + x(0.1 + x))
0.085 + -0.17x = ((0.01 + 0.1x) + x(0.1 + x))
0.085 + -0.17x = (0.01 + 0.1x + (0.1 * x + x * x))
0.085 + -0.17x = (0.01 + 0.1x + (0.1x + x2))

Combine like terms: 0.1x + 0.1x = 0.2x
0.085 + -0.17x = (0.01 + 0.2x + x2)

Solving
0.085 + -0.17x = 0.01 + 0.2x + x2

Solving for variable 'x'.

Reorder the terms:
0.085 + -0.01 + -0.17x + -0.2x + -1x2 = 0.01 + 0.2x + x2 + -0.01 + -0.2x + -1x2

Combine like terms: 0.085 + -0.01 = 0.075
0.075 + -0.17x + -0.2x + -1x2 = 0.01 + 0.2x + x2 + -0.01 + -0.2x + -1x2

Combine like terms: -0.17x + -0.2x = -0.37x
0.075 + -0.37x + -1x2 = 0.01 + 0.2x + x2 + -0.01 + -0.2x + -1x2

Reorder the terms:
0.075 + -0.37x + -1x2 = 0.01 + -0.01 + 0.2x + -0.2x + x2 + -1x2

Combine like terms: 0.01 + -0.01 = 0.00
0.075 + -0.37x + -1x2 = 0.00 + 0.2x + -0.2x + x2 + -1x2
0.075 + -0.37x + -1x2 = 0.2x + -0.2x + x2 + -1x2

Combine like terms: 0.2x + -0.2x = 0.0
0.075 + -0.37x + -1x2 = 0.0 + x2 + -1x2
0.075 + -0.37x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0.075 + -0.37x + -1x2 = 0

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

Divide each side by '-1'.
-0.075 + 0.37x + x2 = 0

Move the constant term to the right:

Add '0.075' to each side of the equation.
-0.075 + 0.37x + 0.075 + x2 = 0 + 0.075

Reorder the terms:
-0.075 + 0.075 + 0.37x + x2 = 0 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + 0.37x + x2 = 0 + 0.075
0.37x + x2 = 0 + 0.075

Combine like terms: 0 + 0.075 = 0.075
0.37x + x2 = 0.075

The x term is 0.37x.  Take half its coefficient (0.185).
Square it (0.034225) and add it to both sides.

Add '0.034225' to each side of the equation.
0.37x + 0.034225 + x2 = 0.075 + 0.034225

Reorder the terms:
0.034225 + 0.37x + x2 = 0.075 + 0.034225

Combine like terms: 0.075 + 0.034225 = 0.109225
0.034225 + 0.37x + x2 = 0.109225

Factor a perfect square on the left side:
(x + 0.185)(x + 0.185) = 0.109225

Calculate the square root of the right side: 0.330492057

Break this problem into two subproblems by setting 
(x + 0.185) equal to 0.330492057 and -0.330492057.

Subproblem 1
x + 0.185 = 0.330492057

Simplifying
x + 0.185 = 0.330492057

Reorder the terms:
0.185 + x = 0.330492057

Solving
0.185 + x = 0.330492057

Solving for variable 'x'.

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

Add '-0.185' to each side of the equation.
0.185 + -0.185 + x = 0.330492057 + -0.185

Combine like terms: 0.185 + -0.185 = 0.000
0.000 + x = 0.330492057 + -0.185
x = 0.330492057 + -0.185

Combine like terms: 0.330492057 + -0.185 = 0.145492057
x = 0.145492057

Simplifying
x = 0.145492057

Subproblem 2
x + 0.185 = -0.330492057

Simplifying
x + 0.185 = -0.330492057

Reorder the terms:
0.185 + x = -0.330492057

Solving
0.185 + x = -0.330492057

Solving for variable 'x'.

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

Add '-0.185' to each side of the equation.
0.185 + -0.185 + x = -0.330492057 + -0.185

Combine like terms: 0.185 + -0.185 = 0.000
0.000 + x = -0.330492057 + -0.185
x = -0.330492057 + -0.185

Combine like terms: -0.330492057 + -0.185 = -0.515492057
x = -0.515492057

Simplifying
x = -0.515492057

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.145492057, -0.515492057}