A^6+32A^3-64=0

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Solution for A^6+32A^3-64=0 equation: 


Simplifying
A6 + 32A3 + -64 = 0

Reorder the terms:
-64 + 32A3 + A6 = 0

Solving
-64 + 32A3 + A6 = 0

Solving for variable 'A'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 32A3 + 64 + A6 = 0 + 64

Reorder the terms:
-64 + 64 + 32A3 + A6 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 32A3 + A6 = 0 + 64
32A3 + A6 = 0 + 64

Combine like terms: 0 + 64 = 64
32A3 + A6 = 64

The A term is 32A3.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32A3 + 256 + A6 = 64 + 256

Reorder the terms:
256 + 32A3 + A6 = 64 + 256

Combine like terms: 64 + 256 = 320
256 + 32A3 + A6 = 320

Factor a perfect square on the left side:
(A3 + 16)(A3 + 16) = 320

Calculate the square root of the right side: 17.88854382

Break this problem into two subproblems by setting 
(A3 + 16) equal to 17.88854382 and -17.88854382.


Subproblem 1
A3 + 16 = 17.88854382

Simplifying
A3 + 16 = 17.88854382

Reorder the terms:
16 + A3 = 17.88854382

Solving
16 + A3 = 17.88854382

Solving for variable 'A'.

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

Add '-16' to each side of the equation.
16 + -16 + A3 = 17.88854382 + -16

Combine like terms: 16 + -16 = 0
0 + A3 = 17.88854382 + -16
A3 = 17.88854382 + -16

Combine like terms: 17.88854382 + -16 = 1.88854382
A3 = 1.88854382

Simplifying
A3 = 1.88854382

Reorder the terms:
-1.88854382 + A3 = 1.88854382 + -1.88854382

Combine like terms: 1.88854382 + -1.88854382 = 0.00000000
-1.88854382 + A3 = 0.00000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
A3 + 16 = -17.88854382

Simplifying
A3 + 16 = -17.88854382

Reorder the terms:
16 + A3 = -17.88854382

Solving
16 + A3 = -17.88854382

Solving for variable 'A'.

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

Add '-16' to each side of the equation.
16 + -16 + A3 = -17.88854382 + -16

Combine like terms: 16 + -16 = 0
0 + A3 = -17.88854382 + -16
A3 = -17.88854382 + -16

Combine like terms: -17.88854382 + -16 = -33.88854382
A3 = -33.88854382

Simplifying
A3 = -33.88854382

Reorder the terms:
33.88854382 + A3 = -33.88854382 + 33.88854382

Combine like terms: -33.88854382 + 33.88854382 = 0.00000000
33.88854382 + A3 = 0.00000000

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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