3z^4+3z^2+2=0

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Solution for 3z^4+3z^2+2=0 equation:


Simplifying
3z4 + 3z2 + 2 = 0

Reorder the terms:
2 + 3z2 + 3z4 = 0

Solving
2 + 3z2 + 3z4 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.6666666667 + z2 + z4 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + z2 + -0.6666666667 + z4 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + z2 + z4 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + z2 + z4 = 0 + -0.6666666667
z2 + z4 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
z2 + z4 = -0.6666666667

The z term is z2.  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.
 + 0.25 + z4 = -0.6666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + z4 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
1.25 + z4 = -0.4166666667

Factor a perfect square on the left side:
(z2 + 0.5)(z2 + 0.5) = -0.4166666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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