A^4+A^2-9=0

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Solution for A^4+A^2-9=0 equation: 


Simplifying
A4 + A2 + -9 = 0

Reorder the terms:
-9 + A2 + A4 = 0

Solving
-9 + A2 + A4 = 0

Solving for variable 'A'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + A2 + 9 + A4 = 0 + 9

Reorder the terms:
-9 + 9 + A2 + A4 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + A2 + A4 = 0 + 9
A2 + A4 = 0 + 9

Combine like terms: 0 + 9 = 9
A2 + A4 = 9

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.
A2 + 0.25 + A4 = 9 + 0.25

Reorder the terms:
0.25 + A2 + A4 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + A2 + A4 = 9.25

Factor a perfect square on the left side:
(A2 + 0.5)(A2 + 0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(A2 + 0.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
A2 + 0.5 = 3.041381265

Simplifying
A2 + 0.5 = 3.041381265

Reorder the terms:
0.5 + A2 = 3.041381265

Solving
0.5 + A2 = 3.041381265

Solving for variable 'A'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + A2 = 3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + A2 = 3.041381265 + -0.5
A2 = 3.041381265 + -0.5

Combine like terms: 3.041381265 + -0.5 = 2.541381265
A2 = 2.541381265

Simplifying
A2 = 2.541381265

Take the square root of each side:
A = {-1.594171028, 1.594171028}


Subproblem 2
A2 + 0.5 = -3.041381265

Simplifying
A2 + 0.5 = -3.041381265

Reorder the terms:
0.5 + A2 = -3.041381265

Solving
0.5 + A2 = -3.041381265

Solving for variable 'A'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + A2 = -3.041381265 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + A2 = -3.041381265 + -0.5
A2 = -3.041381265 + -0.5

Combine like terms: -3.041381265 + -0.5 = -3.541381265
A2 = -3.541381265

Simplifying
A2 = -3.541381265

Reorder the terms:
3.541381265 + A2 = -3.541381265 + 3.541381265

Combine like terms: -3.541381265 + 3.541381265 = 0.000000000
3.541381265 + 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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