0=x^4+2x^2+36

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Solution for 0=x^4+2x^2+36 equation: 


Simplifying
0 = x4 + 2x2 + 36

Reorder the terms:
0 = 36 + 2x2 + x4

Solving
0 = 36 + 2x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -36 = -36
-36 + -2x2 + -1x4 = 36 + 2x2 + x4 + -36 + -2x2 + -1x4

Reorder the terms:
-36 + -2x2 + -1x4 = 36 + -36 + 2x2 + -2x2 + x4 + -1x4

Combine like terms: 36 + -36 = 0
-36 + -2x2 + -1x4 = 0 + 2x2 + -2x2 + x4 + -1x4
-36 + -2x2 + -1x4 = 2x2 + -2x2 + x4 + -1x4

Combine like terms: 2x2 + -2x2 = 0
-36 + -2x2 + -1x4 = 0 + x4 + -1x4
-36 + -2x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-36 + -2x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 2x2 + x4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(36 + 2x2 + x4)' equal to zero and attempt to solve:

Simplifying
36 + 2x2 + x4 = 0

Solving
36 + 2x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 2x2 + -36 + x4 = 0 + -36

Reorder the terms:
36 + -36 + 2x2 + x4 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 2x2 + x4 = 0 + -36
2x2 + x4 = 0 + -36

Combine like terms: 0 + -36 = -36
2x2 + x4 = -36

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = -36 + 1

Reorder the terms:
1 + 2x2 + x4 = -36 + 1

Combine like terms: -36 + 1 = -35
1 + 2x2 + x4 = -35

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -35

Can't calculate square root of the right side.

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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