g^4+12g^2+9=0

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Solution for g^4+12g^2+9=0 equation:


Simplifying
g4 + 12g2 + 9 = 0

Reorder the terms:
9 + 12g2 + g4 = 0

Solving
9 + 12g2 + g4 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 12g2 + -9 + g4 = 0 + -9

Reorder the terms:
9 + -9 + 12g2 + g4 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 12g2 + g4 = 0 + -9
12g2 + g4 = 0 + -9

Combine like terms: 0 + -9 = -9
12g2 + g4 = -9

The g term is 12g2.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12g2 + 36 + g4 = -9 + 36

Reorder the terms:
36 + 12g2 + g4 = -9 + 36

Combine like terms: -9 + 36 = 27
36 + 12g2 + g4 = 27

Factor a perfect square on the left side:
(g2 + 6)(g2 + 6) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(g2 + 6) equal to 5.196152423 and -5.196152423.

Subproblem 1

g2 + 6 = 5.196152423 Simplifying g2 + 6 = 5.196152423 Reorder the terms: 6 + g2 = 5.196152423 Solving 6 + g2 = 5.196152423 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + g2 = 5.196152423 + -6 Combine like terms: 6 + -6 = 0 0 + g2 = 5.196152423 + -6 g2 = 5.196152423 + -6 Combine like terms: 5.196152423 + -6 = -0.803847577 g2 = -0.803847577 Simplifying g2 = -0.803847577 Reorder the terms: 0.803847577 + g2 = -0.803847577 + 0.803847577 Combine like terms: -0.803847577 + 0.803847577 = 0.000000000 0.803847577 + g2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

g2 + 6 = -5.196152423 Simplifying g2 + 6 = -5.196152423 Reorder the terms: 6 + g2 = -5.196152423 Solving 6 + g2 = -5.196152423 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + g2 = -5.196152423 + -6 Combine like terms: 6 + -6 = 0 0 + g2 = -5.196152423 + -6 g2 = -5.196152423 + -6 Combine like terms: -5.196152423 + -6 = -11.196152423 g2 = -11.196152423 Simplifying g2 = -11.196152423 Reorder the terms: 11.196152423 + g2 = -11.196152423 + 11.196152423 Combine like terms: -11.196152423 + 11.196152423 = 0.000000000 11.196152423 + g2 = 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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