0=x^4+6x^2+25

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Solution for 0=x^4+6x^2+25 equation: 


Simplifying
0 = x4 + 6x2 + 25

Reorder the terms:
0 = 25 + 6x2 + x4

Solving
0 = 25 + 6x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -25 = -25
-25 + -6x2 + -1x4 = 25 + 6x2 + x4 + -25 + -6x2 + -1x4

Reorder the terms:
-25 + -6x2 + -1x4 = 25 + -25 + 6x2 + -6x2 + x4 + -1x4

Combine like terms: 25 + -25 = 0
-25 + -6x2 + -1x4 = 0 + 6x2 + -6x2 + x4 + -1x4
-25 + -6x2 + -1x4 = 6x2 + -6x2 + x4 + -1x4

Combine like terms: 6x2 + -6x2 = 0
-25 + -6x2 + -1x4 = 0 + x4 + -1x4
-25 + -6x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-25 + -6x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 6x2 + x4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(25 + 6x2 + x4)' equal to zero and attempt to solve:

Simplifying
25 + 6x2 + x4 = 0

Solving
25 + 6x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 6x2 + -25 + x4 = 0 + -25

Reorder the terms:
25 + -25 + 6x2 + x4 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 6x2 + x4 = 0 + -25
6x2 + x4 = 0 + -25

Combine like terms: 0 + -25 = -25
6x2 + x4 = -25

The x term is 6x2.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x2 + 9 + x4 = -25 + 9

Reorder the terms:
9 + 6x2 + x4 = -25 + 9

Combine like terms: -25 + 9 = -16
9 + 6x2 + x4 = -16

Factor a perfect square on the left side:
(x2 + 3)(x2 + 3) = -16

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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