-0.1x^2+0.1x=-0.06

Solution for -0.1x^2+0.1x=-0.06 equation:

Simplifying
-0.1x2 + 0.1x = -0.06

Reorder the terms:
0.1x + -0.1x2 = -0.06

Solving
0.1x + -0.1x2 = -0.06

Solving for variable 'x'.

Reorder the terms:
0.06 + 0.1x + -0.1x2 = -0.06 + 0.06

Combine like terms: -0.06 + 0.06 = 0.00
0.06 + 0.1x + -0.1x2 = 0.00

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
-0.6 + -1x + x2 = 0.0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1x + 0.6 + x2 = 0.0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1x + x2 = 0.0 + 0.6

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

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

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.6 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
0.25 + -1x + x2 = 0.85

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
x + -0.5 = 0.921954446

Simplifying
x + -0.5 = 0.921954446

Reorder the terms:
-0.5 + x = 0.921954446

Solving
-0.5 + x = 0.921954446

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.921954446 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.921954446 + 0.5
x = 0.921954446 + 0.5

Combine like terms: 0.921954446 + 0.5 = 1.421954446
x = 1.421954446

Simplifying
x = 1.421954446

Subproblem 2
x + -0.5 = -0.921954446

Simplifying
x + -0.5 = -0.921954446

Reorder the terms:
-0.5 + x = -0.921954446

Solving
-0.5 + x = -0.921954446

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.921954446 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.921954446 + 0.5
x = -0.921954446 + 0.5

Combine like terms: -0.921954446 + 0.5 = -0.421954446
x = -0.421954446

Simplifying
x = -0.421954446

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.421954446, -0.421954446}