x^6+14x^3+4=0

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Solution for x^6+14x^3+4=0 equation: 


Simplifying
x6 + 14x3 + 4 = 0

Reorder the terms:
4 + 14x3 + x6 = 0

Solving
4 + 14x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 14x3 + -4 + x6 = 0 + -4

Reorder the terms:
4 + -4 + 14x3 + x6 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 14x3 + x6 = 0 + -4
14x3 + x6 = 0 + -4

Combine like terms: 0 + -4 = -4
14x3 + x6 = -4

The x term is 14x3.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x3 + 49 + x6 = -4 + 49

Reorder the terms:
49 + 14x3 + x6 = -4 + 49

Combine like terms: -4 + 49 = 45
49 + 14x3 + x6 = 45

Factor a perfect square on the left side:
(x3 + 7)(x3 + 7) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x3 + 7) equal to 6.708203933 and -6.708203933.


Subproblem 1
x3 + 7 = 6.708203933

Simplifying
x3 + 7 = 6.708203933

Reorder the terms:
7 + x3 = 6.708203933

Solving
7 + x3 = 6.708203933

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x3 = 6.708203933 + -7

Combine like terms: 7 + -7 = 0
0 + x3 = 6.708203933 + -7
x3 = 6.708203933 + -7

Combine like terms: 6.708203933 + -7 = -0.291796067
x3 = -0.291796067

Simplifying
x3 = -0.291796067

Reorder the terms:
0.291796067 + x3 = -0.291796067 + 0.291796067

Combine like terms: -0.291796067 + 0.291796067 = 0.000000000
0.291796067 + x3 = 0.000000000

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


Subproblem 2
x3 + 7 = -6.708203933

Simplifying
x3 + 7 = -6.708203933

Reorder the terms:
7 + x3 = -6.708203933

Solving
7 + x3 = -6.708203933

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x3 = -6.708203933 + -7

Combine like terms: 7 + -7 = 0
0 + x3 = -6.708203933 + -7
x3 = -6.708203933 + -7

Combine like terms: -6.708203933 + -7 = -13.708203933
x3 = -13.708203933

Simplifying
x3 = -13.708203933

Reorder the terms:
13.708203933 + x3 = -13.708203933 + 13.708203933

Combine like terms: -13.708203933 + 13.708203933 = 0.000000000
13.708203933 + x3 = 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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