(1+x^2)*x^2=0.2

Solution for (1+x^2)*x^2=0.2 equation:

Simplifying
(1 + x2) * x2 = 0.2

Reorder the terms for easier multiplication:
x2(1 + x2) = 0.2
(1 * x2 + x2 * x2) = 0.2
(1x2 + x4) = 0.2

Solving
1x2 + x4 = 0.2

Solving for variable 'x'.

Reorder the terms:
-0.2 + 1x2 + x4 = 0.2 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
-0.2 + 1x2 + x4 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 1x2 + 0.2 + x4 = 0.0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 1x2 + x4 = 0.0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 1x2 + x4 = 0.0 + 0.2
1x2 + x4 = 0.0 + 0.2

Combine like terms: 0.0 + 0.2 = 0.2
1x2 + x4 = 0.2

The x term is 1x2.  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.
x2 + 0.25 + x4 = 0.2 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
0.25 + x2 + x4 = 0.45

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1
x2 + 0.5 = 0.670820393

Simplifying
x2 + 0.5 = 0.670820393

Reorder the terms:
0.5 + x2 = 0.670820393

Solving
0.5 + x2 = 0.670820393

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 + x2 = 0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 0.670820393 + -0.5
x2 = 0.670820393 + -0.5

Combine like terms: 0.670820393 + -0.5 = 0.170820393
x2 = 0.170820393

Simplifying
x2 = 0.170820393

Take the square root of each side:
x = {-0.413304238, 0.413304238}

Subproblem 2
x2 + 0.5 = -0.670820393

Simplifying
x2 + 0.5 = -0.670820393

Reorder the terms:
0.5 + x2 = -0.670820393

Solving
0.5 + x2 = -0.670820393

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 + x2 = -0.670820393 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -0.670820393 + -0.5
x2 = -0.670820393 + -0.5

Combine like terms: -0.670820393 + -0.5 = -1.170820393
x2 = -1.170820393

Simplifying
x2 = -1.170820393

Reorder the terms:
1.170820393 + x2 = -1.170820393 + 1.170820393

Combine like terms: -1.170820393 + 1.170820393 = 0.000000000
1.170820393 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.