x^4-x^2+0.16=0

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Solution for x^4-x^2+0.16=0 equation: 


Simplifying
x4 + -1x2 + 0.16 = 0

Reorder the terms:
0.16 + -1x2 + x4 = 0

Solving
0.16 + -1x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -1x2 + -0.16 + x4 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + -1x2 + x4 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -1x2 + x4 = 0 + -0.16
-1x2 + x4 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
-1x2 + x4 = -0.16

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.
-1x2 + 0.25 + x4 = -0.16 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = -0.16 + 0.25

Combine like terms: -0.16 + 0.25 = 0.09
0.25 + -1x2 + x4 = 0.09

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 0.3 and -0.3.


Subproblem 1
x2 + -0.5 = 0.3

Simplifying
x2 + -0.5 = 0.3

Reorder the terms:
-0.5 + x2 = 0.3

Solving
-0.5 + x2 = 0.3

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 = 0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 0.3 + 0.5
x2 = 0.3 + 0.5

Combine like terms: 0.3 + 0.5 = 0.8
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}


Subproblem 2
x2 + -0.5 = -0.3

Simplifying
x2 + -0.5 = -0.3

Reorder the terms:
-0.5 + x2 = -0.3

Solving
-0.5 + x2 = -0.3

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 = -0.3 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -0.3 + 0.5
x2 = -0.3 + 0.5

Combine like terms: -0.3 + 0.5 = 0.2
x2 = 0.2

Simplifying
x2 = 0.2

Take the square root of each side:
x = {-0.447213596, 0.447213596}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.894427191, 0.894427191, -0.447213596, 0.447213596}

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