-3=x^4+3x^2+2

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Solution for -3=x^4+3x^2+2 equation: 


Simplifying
-3 = x4 + 3x2 + 2

Reorder the terms:
-3 = 2 + 3x2 + x4

Solving
-3 = 2 + 3x2 + x4

Solving for variable 'x'.

Combine like terms: -3 + -2 = -5
-5 + -3x2 + -1x4 = 2 + 3x2 + x4 + -2 + -3x2 + -1x4

Reorder the terms:
-5 + -3x2 + -1x4 = 2 + -2 + 3x2 + -3x2 + x4 + -1x4

Combine like terms: 2 + -2 = 0
-5 + -3x2 + -1x4 = 0 + 3x2 + -3x2 + x4 + -1x4
-5 + -3x2 + -1x4 = 3x2 + -3x2 + x4 + -1x4

Combine like terms: 3x2 + -3x2 = 0
-5 + -3x2 + -1x4 = 0 + x4 + -1x4
-5 + -3x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-5 + -3x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 3x2 + x4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 3x2 + x4)' equal to zero and attempt to solve:

Simplifying
5 + 3x2 + x4 = 0

Solving
5 + 3x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 3x2 + -5 + x4 = 0 + -5

Reorder the terms:
5 + -5 + 3x2 + x4 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x2 + x4 = 0 + -5
3x2 + x4 = 0 + -5

Combine like terms: 0 + -5 = -5
3x2 + x4 = -5

The x term is 3x2.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x2 + 2.25 + x4 = -5 + 2.25

Reorder the terms:
2.25 + 3x2 + x4 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + 3x2 + x4 = -2.75

Factor a perfect square on the left side:
(x2 + 1.5)(x2 + 1.5) = -2.75

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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