216x^6+279x^3-27=0

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Solution for 216x^6+279x^3-27=0 equation: 


Simplifying
216x6 + 279x3 + -27 = 0

Reorder the terms:
-27 + 279x3 + 216x6 = 0

Solving
-27 + 279x3 + 216x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + 31x3 + 24x6) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-3 + 31x3 + 24x6)' equal to zero and attempt to solve:

Simplifying
-3 + 31x3 + 24x6 = 0

Solving
-3 + 31x3 + 24x6 = 0

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

Divide each side by '24'.
-0.125 + 1.291666667x3 + x6 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 1.291666667x3 + 0.125 + x6 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 1.291666667x3 + x6 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 1.291666667x3 + x6 = 0 + 0.125
1.291666667x3 + x6 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
1.291666667x3 + x6 = 0.125

The x term is 1.291666667x3.  Take half its coefficient (0.6458333335).
Square it (0.4171006947) and add it to both sides.

Add '0.4171006947' to each side of the equation.
1.291666667x3 + 0.4171006947 + x6 = 0.125 + 0.4171006947

Reorder the terms:
0.4171006947 + 1.291666667x3 + x6 = 0.125 + 0.4171006947

Combine like terms: 0.125 + 0.4171006947 = 0.5421006947
0.4171006947 + 1.291666667x3 + x6 = 0.5421006947

Factor a perfect square on the left side:
(x3 + 0.6458333335)(x3 + 0.6458333335) = 0.5421006947

Calculate the square root of the right side: 0.736274877

Break this problem into two subproblems by setting 
(x3 + 0.6458333335) equal to 0.736274877 and -0.736274877.


Subproblem 1
x3 + 0.6458333335 = 0.736274877

Simplifying
x3 + 0.6458333335 = 0.736274877

Reorder the terms:
0.6458333335 + x3 = 0.736274877

Solving
0.6458333335 + x3 = 0.736274877

Solving for variable 'x'.

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

Add '-0.6458333335' to each side of the equation.
0.6458333335 + -0.6458333335 + x3 = 0.736274877 + -0.6458333335

Combine like terms: 0.6458333335 + -0.6458333335 = 0.0000000000
0.0000000000 + x3 = 0.736274877 + -0.6458333335
x3 = 0.736274877 + -0.6458333335

Combine like terms: 0.736274877 + -0.6458333335 = 0.0904415435
x3 = 0.0904415435

Simplifying
x3 = 0.0904415435

Reorder the terms:
-0.0904415435 + x3 = 0.0904415435 + -0.0904415435

Combine like terms: 0.0904415435 + -0.0904415435 = 0.0000000000
-0.0904415435 + x3 = 0.0000000000

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


Subproblem 2
x3 + 0.6458333335 = -0.736274877

Simplifying
x3 + 0.6458333335 = -0.736274877

Reorder the terms:
0.6458333335 + x3 = -0.736274877

Solving
0.6458333335 + x3 = -0.736274877

Solving for variable 'x'.

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

Add '-0.6458333335' to each side of the equation.
0.6458333335 + -0.6458333335 + x3 = -0.736274877 + -0.6458333335

Combine like terms: 0.6458333335 + -0.6458333335 = 0.0000000000
0.0000000000 + x3 = -0.736274877 + -0.6458333335
x3 = -0.736274877 + -0.6458333335

Combine like terms: -0.736274877 + -0.6458333335 = -1.3821082105
x3 = -1.3821082105

Simplifying
x3 = -1.3821082105

Reorder the terms:
1.3821082105 + x3 = -1.3821082105 + 1.3821082105

Combine like terms: -1.3821082105 + 1.3821082105 = 0.0000000000
1.3821082105 + x3 = 0.0000000000

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.

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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