3a^4-9a^2-12=10

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Solution for 3a^4-9a^2-12=10 equation: 


Simplifying
3a4 + -9a2 + -12 = 10

Reorder the terms:
-12 + -9a2 + 3a4 = 10

Solving
-12 + -9a2 + 3a4 = 10

Solving for variable 'a'.

Reorder the terms:
-12 + -10 + -9a2 + 3a4 = 10 + -10

Combine like terms: -12 + -10 = -22
-22 + -9a2 + 3a4 = 10 + -10

Combine like terms: 10 + -10 = 0
-22 + -9a2 + 3a4 = 0

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

Divide each side by '3'.
-7.333333333 + -3a2 + a4 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + -3a2 + 7.333333333 + a4 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + -3a2 + a4 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + -3a2 + a4 = 0 + 7.333333333
-3a2 + a4 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
-3a2 + a4 = 7.333333333

The a term is -3a2.  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.
-3a2 + 2.25 + a4 = 7.333333333 + 2.25

Reorder the terms:
2.25 + -3a2 + a4 = 7.333333333 + 2.25

Combine like terms: 7.333333333 + 2.25 = 9.583333333
2.25 + -3a2 + a4 = 9.583333333

Factor a perfect square on the left side:
(a2 + -1.5)(a2 + -1.5) = 9.583333333

Calculate the square root of the right side: 3.095695937

Break this problem into two subproblems by setting 
(a2 + -1.5) equal to 3.095695937 and -3.095695937.


Subproblem 1
a2 + -1.5 = 3.095695937

Simplifying
a2 + -1.5 = 3.095695937

Reorder the terms:
-1.5 + a2 = 3.095695937

Solving
-1.5 + a2 = 3.095695937

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a2 = 3.095695937 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a2 = 3.095695937 + 1.5
a2 = 3.095695937 + 1.5

Combine like terms: 3.095695937 + 1.5 = 4.595695937
a2 = 4.595695937

Simplifying
a2 = 4.595695937

Take the square root of each side:
a = {-2.143757434, 2.143757434}


Subproblem 2
a2 + -1.5 = -3.095695937

Simplifying
a2 + -1.5 = -3.095695937

Reorder the terms:
-1.5 + a2 = -3.095695937

Solving
-1.5 + a2 = -3.095695937

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a2 = -3.095695937 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a2 = -3.095695937 + 1.5
a2 = -3.095695937 + 1.5

Combine like terms: -3.095695937 + 1.5 = -1.595695937
a2 = -1.595695937

Simplifying
a2 = -1.595695937

Reorder the terms:
1.595695937 + a2 = -1.595695937 + 1.595695937

Combine like terms: -1.595695937 + 1.595695937 = 0.000000000
1.595695937 + a2 = 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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