3a^2-7a^4=9-a^4

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Solution for 3a^2-7a^4=9-a^4 equation: 


Simplifying
3a2 + -7a4 = 9 + -1a4

Solving
3a2 + -7a4 = 9 + -1a4

Solving for variable 'a'.

Reorder the terms:
-9 + 3a2 + -7a4 + a4 = 9 + -1a4 + -9 + a4

Combine like terms: -7a4 + a4 = -6a4
-9 + 3a2 + -6a4 = 9 + -1a4 + -9 + a4

Reorder the terms:
-9 + 3a2 + -6a4 = 9 + -9 + -1a4 + a4

Combine like terms: 9 + -9 = 0
-9 + 3a2 + -6a4 = 0 + -1a4 + a4
-9 + 3a2 + -6a4 = -1a4 + a4

Combine like terms: -1a4 + a4 = 0
-9 + 3a2 + -6a4 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + a2 + -2a4) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + a2 + -2a4)' equal to zero and attempt to solve:

Simplifying
-3 + a2 + -2a4 = 0

Solving
-3 + a2 + -2a4 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -0.5a2 + a4 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5a2 + -1.5 + a4 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5a2 + a4 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5a2 + a4 = 0 + -1.5
-0.5a2 + a4 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5a2 + a4 = -1.5

The a term is a2.  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.
-0.5a2 + 0.25 + a4 = -1.5 + 0.25

Reorder the terms:
0.25 + -0.5a2 + a4 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -0.5a2 + a4 = -1.25

Factor a perfect square on the left side:
(a2 + 0.5)(a2 + 0.5) = -1.25

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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