x^4+x^2=512

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Solution for x^4+x^2=512 equation: 


Simplifying
x4 + x2 = 512

Reorder the terms:
x2 + x4 = 512

Solving
x2 + x4 = 512

Solving for variable 'x'.

Reorder the terms:
-512 + x2 + x4 = 512 + -512

Combine like terms: 512 + -512 = 0
-512 + x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '512' to each side of the equation.
-512 + x2 + 512 + x4 = 0 + 512

Reorder the terms:
-512 + 512 + x2 + x4 = 0 + 512

Combine like terms: -512 + 512 = 0
0 + x2 + x4 = 0 + 512
x2 + x4 = 0 + 512

Combine like terms: 0 + 512 = 512
x2 + x4 = 512

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 = 512 + 0.25

Reorder the terms:
0.25 + x2 + x4 = 512 + 0.25

Combine like terms: 512 + 0.25 = 512.25
0.25 + x2 + x4 = 512.25

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 512.25

Calculate the square root of the right side: 22.632940596

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 22.632940596 and -22.632940596.


Subproblem 1
x2 + 0.5 = 22.632940596

Simplifying
x2 + 0.5 = 22.632940596

Reorder the terms:
0.5 + x2 = 22.632940596

Solving
0.5 + x2 = 22.632940596

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 = 22.632940596 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 22.632940596 + -0.5
x2 = 22.632940596 + -0.5

Combine like terms: 22.632940596 + -0.5 = 22.132940596
x2 = 22.132940596

Simplifying
x2 = 22.132940596

Take the square root of each side:
x = {-4.704565931, 4.704565931}


Subproblem 2
x2 + 0.5 = -22.632940596

Simplifying
x2 + 0.5 = -22.632940596

Reorder the terms:
0.5 + x2 = -22.632940596

Solving
0.5 + x2 = -22.632940596

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 = -22.632940596 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -22.632940596 + -0.5
x2 = -22.632940596 + -0.5

Combine like terms: -22.632940596 + -0.5 = -23.132940596
x2 = -23.132940596

Simplifying
x2 = -23.132940596

Reorder the terms:
23.132940596 + x2 = -23.132940596 + 23.132940596

Combine like terms: -23.132940596 + 23.132940596 = 0.000000000
23.132940596 + 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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