x^6+14x^3=16

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Solution for x^6+14x^3=16 equation: 


Simplifying
x6 + 14x3 = 16

Reorder the terms:
14x3 + x6 = 16

Solving
14x3 + x6 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 14x3 + x6 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 14x3 + x6 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 14x3 + 16 + x6 = 0 + 16

Reorder the terms:
-16 + 16 + 14x3 + x6 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 14x3 + x6 = 0 + 16
14x3 + x6 = 0 + 16

Combine like terms: 0 + 16 = 16
14x3 + x6 = 16

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 = 16 + 49

Reorder the terms:
49 + 14x3 + x6 = 16 + 49

Combine like terms: 16 + 49 = 65
49 + 14x3 + x6 = 65

Factor a perfect square on the left side:
(x3 + 7)(x3 + 7) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x3 + 7) equal to 8.062257748 and -8.062257748.


Subproblem 1
x3 + 7 = 8.062257748

Simplifying
x3 + 7 = 8.062257748

Reorder the terms:
7 + x3 = 8.062257748

Solving
7 + x3 = 8.062257748

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 = 8.062257748 + -7

Combine like terms: 7 + -7 = 0
0 + x3 = 8.062257748 + -7
x3 = 8.062257748 + -7

Combine like terms: 8.062257748 + -7 = 1.062257748
x3 = 1.062257748

Simplifying
x3 = 1.062257748

Reorder the terms:
-1.062257748 + x3 = 1.062257748 + -1.062257748

Combine like terms: 1.062257748 + -1.062257748 = 0.000000000
-1.062257748 + 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 = -8.062257748

Simplifying
x3 + 7 = -8.062257748

Reorder the terms:
7 + x3 = -8.062257748

Solving
7 + x3 = -8.062257748

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 = -8.062257748 + -7

Combine like terms: 7 + -7 = 0
0 + x3 = -8.062257748 + -7
x3 = -8.062257748 + -7

Combine like terms: -8.062257748 + -7 = -15.062257748
x3 = -15.062257748

Simplifying
x3 = -15.062257748

Reorder the terms:
15.062257748 + x3 = -15.062257748 + 15.062257748

Combine like terms: -15.062257748 + 15.062257748 = 0.000000000
15.062257748 + 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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