-0.2x^2+0.1x+0.04=0

Solution for -0.2x^2+0.1x+0.04=0 equation:

Simplifying
-0.2x2 + 0.1x + 0.04 = 0

Reorder the terms:
0.04 + 0.1x + -0.2x2 = 0

Solving
0.04 + 0.1x + -0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '-0.2'.
-0.2 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.5x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.5x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.5x + x2 = 0 + 0.2
-0.5x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.5x + x2 = 0.2

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 = 0.2 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.2 + 0.0625

Combine like terms: 0.2 + 0.0625 = 0.2625
0.0625 + -0.5x + x2 = 0.2625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.2625

Calculate the square root of the right side: 0.512347538

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.512347538 and -0.512347538.

Subproblem 1
x + -0.25 = 0.512347538

Simplifying
x + -0.25 = 0.512347538

Reorder the terms:
-0.25 + x = 0.512347538

Solving
-0.25 + x = 0.512347538

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 = 0.512347538 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.512347538 + 0.25
x = 0.512347538 + 0.25

Combine like terms: 0.512347538 + 0.25 = 0.762347538
x = 0.762347538

Simplifying
x = 0.762347538

Subproblem 2
x + -0.25 = -0.512347538

Simplifying
x + -0.25 = -0.512347538

Reorder the terms:
-0.25 + x = -0.512347538

Solving
-0.25 + x = -0.512347538

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 = -0.512347538 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.512347538 + 0.25
x = -0.512347538 + 0.25

Combine like terms: -0.512347538 + 0.25 = -0.262347538
x = -0.262347538

Simplifying
x = -0.262347538

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.762347538, -0.262347538}