a^6+8a^3=-27

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Solution for a^6+8a^3=-27 equation: 


Simplifying
a6 + 8a3 = -27

Reorder the terms:
8a3 + a6 = -27

Solving
8a3 + a6 = -27

Solving for variable 'a'.

Reorder the terms:
27 + 8a3 + a6 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 8a3 + a6 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 8a3 + -27 + a6 = 0 + -27

Reorder the terms:
27 + -27 + 8a3 + a6 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 8a3 + a6 = 0 + -27
8a3 + a6 = 0 + -27

Combine like terms: 0 + -27 = -27
8a3 + a6 = -27

The a term is 8a3.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8a3 + 16 + a6 = -27 + 16

Reorder the terms:
16 + 8a3 + a6 = -27 + 16

Combine like terms: -27 + 16 = -11
16 + 8a3 + a6 = -11

Factor a perfect square on the left side:
(a3 + 4)(a3 + 4) = -11

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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