-0.2x^2+0.1x=-0.03

Solution for -0.2x^2+0.1x=-0.03 equation:

Simplifying
-0.2x2 + 0.1x = -0.03

Reorder the terms:
0.1x + -0.2x2 = -0.03

Solving
0.1x + -0.2x2 = -0.03

Solving for variable 'x'.

Reorder the terms:
0.03 + 0.1x + -0.2x2 = -0.03 + 0.03

Combine like terms: -0.03 + 0.03 = 0.00
0.03 + 0.1x + -0.2x2 = 0.00

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
-0.15 + -0.5x + x2 = 0.0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + -0.5x + 0.15 + x2 = 0.0 + 0.15

Reorder the terms:
-0.15 + 0.15 + -0.5x + x2 = 0.0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + -0.5x + x2 = 0.0 + 0.15
-0.5x + x2 = 0.0 + 0.15

Combine like terms: 0.0 + 0.15 = 0.15
-0.5x + x2 = 0.15

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 = 0.15 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.15 + 0.0625

Combine like terms: 0.15 + 0.0625 = 0.2125
0.0625 + -0.5x + x2 = 0.2125

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.2125

Calculate the square root of the right side: 0.460977223

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.460977223 and -0.460977223.

Subproblem 1
x + -0.25 = 0.460977223

Simplifying
x + -0.25 = 0.460977223

Reorder the terms:
-0.25 + x = 0.460977223

Solving
-0.25 + x = 0.460977223

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 = 0.460977223 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.460977223 + 0.25
x = 0.460977223 + 0.25

Combine like terms: 0.460977223 + 0.25 = 0.710977223
x = 0.710977223

Simplifying
x = 0.710977223

Subproblem 2
x + -0.25 = -0.460977223

Simplifying
x + -0.25 = -0.460977223

Reorder the terms:
-0.25 + x = -0.460977223

Solving
-0.25 + x = -0.460977223

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 = -0.460977223 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.460977223 + 0.25
x = -0.460977223 + 0.25

Combine like terms: -0.460977223 + 0.25 = -0.210977223
x = -0.210977223

Simplifying
x = -0.210977223

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.710977223, -0.210977223}