x^4-x^2=0.26

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Solution for x^4-x^2=0.26 equation: 


Simplifying
x4 + -1x2 = 0.26

Reorder the terms:
-1x2 + x4 = 0.26

Solving
-1x2 + x4 = 0.26

Solving for variable 'x'.

Reorder the terms:
-0.26 + -1x2 + x4 = 0.26 + -0.26

Combine like terms: 0.26 + -0.26 = 0.00
-0.26 + -1x2 + x4 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.26' to each side of the equation.
-0.26 + -1x2 + 0.26 + x4 = 0.00 + 0.26

Reorder the terms:
-0.26 + 0.26 + -1x2 + x4 = 0.00 + 0.26

Combine like terms: -0.26 + 0.26 = 0.00
0.00 + -1x2 + x4 = 0.00 + 0.26
-1x2 + x4 = 0.00 + 0.26

Combine like terms: 0.00 + 0.26 = 0.26
-1x2 + x4 = 0.26

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 = 0.26 + 0.25

Reorder the terms:
0.25 + -1x2 + x4 = 0.26 + 0.25

Combine like terms: 0.26 + 0.25 = 0.51
0.25 + -1x2 + x4 = 0.51

Factor a perfect square on the left side:
(x2 + -0.5)(x2 + -0.5) = 0.51

Calculate the square root of the right side: 0.714142843

Break this problem into two subproblems by setting 
(x2 + -0.5) equal to 0.714142843 and -0.714142843.


Subproblem 1
x2 + -0.5 = 0.714142843

Simplifying
x2 + -0.5 = 0.714142843

Reorder the terms:
-0.5 + x2 = 0.714142843

Solving
-0.5 + x2 = 0.714142843

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 = 0.714142843 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = 0.714142843 + 0.5
x2 = 0.714142843 + 0.5

Combine like terms: 0.714142843 + 0.5 = 1.214142843
x2 = 1.214142843

Simplifying
x2 = 1.214142843

Take the square root of each side:
x = {-1.101881501, 1.101881501}


Subproblem 2
x2 + -0.5 = -0.714142843

Simplifying
x2 + -0.5 = -0.714142843

Reorder the terms:
-0.5 + x2 = -0.714142843

Solving
-0.5 + x2 = -0.714142843

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 = -0.714142843 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x2 = -0.714142843 + 0.5
x2 = -0.714142843 + 0.5

Combine like terms: -0.714142843 + 0.5 = -0.214142843
x2 = -0.214142843

Simplifying
x2 = -0.214142843

Reorder the terms:
0.214142843 + x2 = -0.214142843 + 0.214142843

Combine like terms: -0.214142843 + 0.214142843 = 0.000000000
0.214142843 + 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.

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