x^2-0.6x=0.2

Solution for x^2-0.6x=0.2 equation:

Simplifying
x2 + -0.6x = 0.2

Reorder the terms:
-0.6x + x2 = 0.2

Solving
-0.6x + x2 = 0.2

Solving for variable 'x'.

Reorder the terms:
-0.2 + -0.6x + x2 = 0.2 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + -0.6x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.6x + 0.2 + x2 = 0.0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.6x + x2 = 0.0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.6x + x2 = 0.0 + 0.2
-0.6x + x2 = 0.0 + 0.2

Combine like terms: 0.0 + 0.2 = 0.2
-0.6x + x2 = 0.2

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 0.2 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 0.2 + 0.09

Combine like terms: 0.2 + 0.09 = 0.29
0.09 + -0.6x + x2 = 0.29

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.29

Calculate the square root of the right side: 0.538516481

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.538516481 and -0.538516481.

Subproblem 1
x + -0.3 = 0.538516481

Simplifying
x + -0.3 = 0.538516481

Reorder the terms:
-0.3 + x = 0.538516481

Solving
-0.3 + x = 0.538516481

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 0.538516481 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 0.538516481 + 0.3
x = 0.538516481 + 0.3

Combine like terms: 0.538516481 + 0.3 = 0.838516481
x = 0.838516481

Simplifying
x = 0.838516481

Subproblem 2
x + -0.3 = -0.538516481

Simplifying
x + -0.3 = -0.538516481

Reorder the terms:
-0.3 + x = -0.538516481

Solving
-0.3 + x = -0.538516481

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -0.538516481 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -0.538516481 + 0.3
x = -0.538516481 + 0.3

Combine like terms: -0.538516481 + 0.3 = -0.238516481
x = -0.238516481

Simplifying
x = -0.238516481

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.838516481, -0.238516481}