0.17(0.2+x)=(0.3-x)(0.3-x)

Solution for 0.17(0.2+x)=(0.3-x)(0.3-x) equation:

Simplifying
0.17(0.2 + x) = (0.3 + -1x)(0.3 + -1x)
(0.2 * 0.17 + x * 0.17) = (0.3 + -1x)(0.3 + -1x)
(0.034 + 0.17x) = (0.3 + -1x)(0.3 + -1x)

Multiply (0.3 + -1x) * (0.3 + -1x)
0.034 + 0.17x = (0.3(0.3 + -1x) + -1x * (0.3 + -1x))
0.034 + 0.17x = ((0.3 * 0.3 + -1x * 0.3) + -1x * (0.3 + -1x))
0.034 + 0.17x = ((0.09 + -0.3x) + -1x * (0.3 + -1x))
0.034 + 0.17x = (0.09 + -0.3x + (0.3 * -1x + -1x * -1x))
0.034 + 0.17x = (0.09 + -0.3x + (-0.3x + 1x2))

Combine like terms: -0.3x + -0.3x = -0.6x
0.034 + 0.17x = (0.09 + -0.6x + 1x2)

Solving
0.034 + 0.17x = 0.09 + -0.6x + 1x2

Solving for variable 'x'.

Reorder the terms:
0.034 + -0.09 + 0.17x + 0.6x + -1x2 = 0.09 + -0.6x + 1x2 + -0.09 + 0.6x + -1x2

Combine like terms: 0.034 + -0.09 = -0.056
-0.056 + 0.17x + 0.6x + -1x2 = 0.09 + -0.6x + 1x2 + -0.09 + 0.6x + -1x2

Combine like terms: 0.17x + 0.6x = 0.77x
-0.056 + 0.77x + -1x2 = 0.09 + -0.6x + 1x2 + -0.09 + 0.6x + -1x2

Reorder the terms:
-0.056 + 0.77x + -1x2 = 0.09 + -0.09 + -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: 0.09 + -0.09 = 0.00
-0.056 + 0.77x + -1x2 = 0.00 + -0.6x + 0.6x + 1x2 + -1x2
-0.056 + 0.77x + -1x2 = -0.6x + 0.6x + 1x2 + -1x2

Combine like terms: -0.6x + 0.6x = 0.0
-0.056 + 0.77x + -1x2 = 0.0 + 1x2 + -1x2
-0.056 + 0.77x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-0.056 + 0.77x + -1x2 = 0

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

Divide each side by '-1'.
0.056 + -0.77x + x2 = 0

Move the constant term to the right:

Add '-0.056' to each side of the equation.
0.056 + -0.77x + -0.056 + x2 = 0 + -0.056

Reorder the terms:
0.056 + -0.056 + -0.77x + x2 = 0 + -0.056

Combine like terms: 0.056 + -0.056 = 0.000
0.000 + -0.77x + x2 = 0 + -0.056
-0.77x + x2 = 0 + -0.056

Combine like terms: 0 + -0.056 = -0.056
-0.77x + x2 = -0.056

The x term is -0.77x.  Take half its coefficient (-0.385).
Square it (0.148225) and add it to both sides.

Add '0.148225' to each side of the equation.
-0.77x + 0.148225 + x2 = -0.056 + 0.148225

Reorder the terms:
0.148225 + -0.77x + x2 = -0.056 + 0.148225

Combine like terms: -0.056 + 0.148225 = 0.092225
0.148225 + -0.77x + x2 = 0.092225

Factor a perfect square on the left side:
(x + -0.385)(x + -0.385) = 0.092225

Calculate the square root of the right side: 0.303685693

Break this problem into two subproblems by setting 
(x + -0.385) equal to 0.303685693 and -0.303685693.

Subproblem 1
x + -0.385 = 0.303685693

Simplifying
x + -0.385 = 0.303685693

Reorder the terms:
-0.385 + x = 0.303685693

Solving
-0.385 + x = 0.303685693

Solving for variable 'x'.

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

Add '0.385' to each side of the equation.
-0.385 + 0.385 + x = 0.303685693 + 0.385

Combine like terms: -0.385 + 0.385 = 0.000
0.000 + x = 0.303685693 + 0.385
x = 0.303685693 + 0.385

Combine like terms: 0.303685693 + 0.385 = 0.688685693
x = 0.688685693

Simplifying
x = 0.688685693

Subproblem 2
x + -0.385 = -0.303685693

Simplifying
x + -0.385 = -0.303685693

Reorder the terms:
-0.385 + x = -0.303685693

Solving
-0.385 + x = -0.303685693

Solving for variable 'x'.

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

Add '0.385' to each side of the equation.
-0.385 + 0.385 + x = -0.303685693 + 0.385

Combine like terms: -0.385 + 0.385 = 0.000
0.000 + x = -0.303685693 + 0.385
x = -0.303685693 + 0.385

Combine like terms: -0.303685693 + 0.385 = 0.081314307
x = 0.081314307

Simplifying
x = 0.081314307

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.688685693, 0.081314307}