2x^2=0.10(x^2-0.400x+0.04)

Solution for 2x^2=0.10(x^2-0.400x+0.04) equation:

Simplifying
2x2 = 0.10(x2 + -0.400x + 0.04)

Reorder the terms:
2x2 = 0.10(0.04 + -0.400x + x2)
2x2 = (0.04 * 0.10 + -0.400x * 0.10 + x2 * 0.10)
2x2 = (0.004 + -0.04x + 0.10x2)

Solving
2x2 = 0.004 + -0.04x + 0.10x2

Solving for variable 'x'.

Reorder the terms:
-0.004 + 0.04x + 2x2 + -0.10x2 = 0.004 + -0.04x + 0.10x2 + -0.004 + 0.04x + -0.10x2

Combine like terms: 2x2 + -0.10x2 = 1.9x2
-0.004 + 0.04x + 1.9x2 = 0.004 + -0.04x + 0.10x2 + -0.004 + 0.04x + -0.10x2

Reorder the terms:
-0.004 + 0.04x + 1.9x2 = 0.004 + -0.004 + -0.04x + 0.04x + 0.10x2 + -0.10x2

Combine like terms: 0.004 + -0.004 = 0.000
-0.004 + 0.04x + 1.9x2 = 0.000 + -0.04x + 0.04x + 0.10x2 + -0.10x2
-0.004 + 0.04x + 1.9x2 = -0.04x + 0.04x + 0.10x2 + -0.10x2

Combine like terms: -0.04x + 0.04x = 0.00
-0.004 + 0.04x + 1.9x2 = 0.00 + 0.10x2 + -0.10x2
-0.004 + 0.04x + 1.9x2 = 0.10x2 + -0.10x2

Combine like terms: 0.10x2 + -0.10x2 = 0.00
-0.004 + 0.04x + 1.9x2 = 0.00

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

Divide each side by '1.9'.
-0.002105263158 + 0.02105263158x + x2 = 0.0

Move the constant term to the right:

Add '0.002105263158' to each side of the equation.
-0.002105263158 + 0.02105263158x + 0.002105263158 + x2 = 0.0 + 0.002105263158

Reorder the terms:
-0.002105263158 + 0.002105263158 + 0.02105263158x + x2 = 0.0 + 0.002105263158

Combine like terms: -0.002105263158 + 0.002105263158 = 0.000000000000
0.000000000000 + 0.02105263158x + x2 = 0.0 + 0.002105263158
0.02105263158x + x2 = 0.0 + 0.002105263158

Combine like terms: 0.0 + 0.002105263158 = 0.002105263158
0.02105263158x + x2 = 0.002105263158

The x term is 0.02105263158x.  Take half its coefficient (0.01052631579).
Square it (0.0001108033241) and add it to both sides.

Add '0.0001108033241' to each side of the equation.
0.02105263158x + 0.0001108033241 + x2 = 0.002105263158 + 0.0001108033241

Reorder the terms:
0.0001108033241 + 0.02105263158x + x2 = 0.002105263158 + 0.0001108033241

Combine like terms: 0.002105263158 + 0.0001108033241 = 0.0022160664821
0.0001108033241 + 0.02105263158x + x2 = 0.0022160664821

Factor a perfect square on the left side:
(x + 0.01052631579)(x + 0.01052631579) = 0.0022160664821

Calculate the square root of the right side: 0.047075115

Break this problem into two subproblems by setting 
(x + 0.01052631579) equal to 0.047075115 and -0.047075115.

Subproblem 1
x + 0.01052631579 = 0.047075115

Simplifying
x + 0.01052631579 = 0.047075115

Reorder the terms:
0.01052631579 + x = 0.047075115

Solving
0.01052631579 + x = 0.047075115

Solving for variable 'x'.

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

Add '-0.01052631579' to each side of the equation.
0.01052631579 + -0.01052631579 + x = 0.047075115 + -0.01052631579

Combine like terms: 0.01052631579 + -0.01052631579 = 0.00000000000
0.00000000000 + x = 0.047075115 + -0.01052631579
x = 0.047075115 + -0.01052631579

Combine like terms: 0.047075115 + -0.01052631579 = 0.03654879921
x = 0.03654879921

Simplifying
x = 0.03654879921

Subproblem 2
x + 0.01052631579 = -0.047075115

Simplifying
x + 0.01052631579 = -0.047075115

Reorder the terms:
0.01052631579 + x = -0.047075115

Solving
0.01052631579 + x = -0.047075115

Solving for variable 'x'.

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

Add '-0.01052631579' to each side of the equation.
0.01052631579 + -0.01052631579 + x = -0.047075115 + -0.01052631579

Combine like terms: 0.01052631579 + -0.01052631579 = 0.00000000000
0.00000000000 + x = -0.047075115 + -0.01052631579
x = -0.047075115 + -0.01052631579

Combine like terms: -0.047075115 + -0.01052631579 = -0.05760143079
x = -0.05760143079

Simplifying
x = -0.05760143079

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.03654879921, -0.05760143079}