x^4+x^2=0.9

Solution for x^4+x^2=0.9 equation:

Simplifying
x4 + x2 = 0.9

Reorder the terms:
x2 + x4 = 0.9

Solving
x2 + x4 = 0.9

Solving for variable 'x'.

Reorder the terms:
-0.9 + x2 + x4 = 0.9 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
-0.9 + x2 + x4 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + x2 + 0.9 + x4 = 0.0 + 0.9

Reorder the terms:
-0.9 + 0.9 + x2 + x4 = 0.0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + x2 + x4 = 0.0 + 0.9
x2 + x4 = 0.0 + 0.9

Combine like terms: 0.0 + 0.9 = 0.9
x2 + x4 = 0.9

The x term is x2.  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 = 0.9 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 0.9 + 0.25

Combine like terms: 0.9 + 0.25 = 1.15
0.25 + x2 + x4 = 1.15

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 1.15

Calculate the square root of the right side: 1.072380529

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 1.072380529 and -1.072380529.

Subproblem 1
x2 + 0.5 = 1.072380529

Simplifying
x2 + 0.5 = 1.072380529

Reorder the terms:
0.5 + x2 = 1.072380529

Solving
0.5 + x2 = 1.072380529

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 = 1.072380529 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 1.072380529 + -0.5
x2 = 1.072380529 + -0.5

Combine like terms: 1.072380529 + -0.5 = 0.572380529
x2 = 0.572380529

Simplifying
x2 = 0.572380529

Take the square root of each side:
x = {-0.756558345, 0.756558345}

Subproblem 2
x2 + 0.5 = -1.072380529

Simplifying
x2 + 0.5 = -1.072380529

Reorder the terms:
0.5 + x2 = -1.072380529

Solving
0.5 + x2 = -1.072380529

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 = -1.072380529 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -1.072380529 + -0.5
x2 = -1.072380529 + -0.5

Combine like terms: -1.072380529 + -0.5 = -1.572380529
x2 = -1.572380529

Simplifying
x2 = -1.572380529

Reorder the terms:
1.572380529 + x2 = -1.572380529 + 1.572380529

Combine like terms: -1.572380529 + 1.572380529 = 0.000000000
1.572380529 + 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.