0.2x^2=0.4x+0.2

Solution for 0.2x^2=0.4x+0.2 equation:

Simplifying
0.2x2 = 0.4x + 0.2

Reorder the terms:
0.2x2 = 0.2 + 0.4x

Solving
0.2x2 = 0.2 + 0.4x

Solving for variable 'x'.

Reorder the terms:
-0.2 + -0.4x + 0.2x2 = 0.2 + 0.4x + -0.2 + -0.4x

Reorder the terms:
-0.2 + -0.4x + 0.2x2 = 0.2 + -0.2 + 0.4x + -0.4x

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + -0.4x + 0.2x2 = 0.0 + 0.4x + -0.4x
-0.2 + -0.4x + 0.2x2 = 0.4x + -0.4x

Combine like terms: 0.4x + -0.4x = 0.0
-0.2 + -0.4x + 0.2x2 = 0.0

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

Divide each side by '0.2'.
-1 + -2x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x + x2 = 0 + 1
-2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2x + x2 = 1

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1 + 1

Reorder the terms:
1 + -2x + x2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + -2x + x2 = 2

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
x + -1 = 1.414213562

Simplifying
x + -1 = 1.414213562

Reorder the terms:
-1 + x = 1.414213562

Solving
-1 + x = 1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.414213562 + 1
x = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
x = 2.414213562

Simplifying
x = 2.414213562

Subproblem 2
x + -1 = -1.414213562

Simplifying
x + -1 = -1.414213562

Reorder the terms:
-1 + x = -1.414213562

Solving
-1 + x = -1.414213562

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.414213562 + 1
x = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
x = -0.414213562

Simplifying
x = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.414213562, -0.414213562}