16x^6+x^3-16=0

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Solution for 16x^6+x^3-16=0 equation: 


Simplifying
16x6 + x3 + -16 = 0

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

Solving
-16 + x3 + 16x6 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
-1 + 0.0625x3 + x6 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.0625x3 + 1 + x6 = 0 + 1

Reorder the terms:
-1 + 1 + 0.0625x3 + x6 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.0625x3 + x6 = 0 + 1
0.0625x3 + x6 = 0 + 1

Combine like terms: 0 + 1 = 1
0.0625x3 + x6 = 1

The x term is x3.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.0625x3 + 0.25 + x6 = 1 + 0.25

Reorder the terms:
0.25 + 0.0625x3 + x6 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + 0.0625x3 + x6 = 1.25

Factor a perfect square on the left side:
(x3 + 0.5)(x3 + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x3 + 0.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
x3 + 0.5 = 1.118033989

Simplifying
x3 + 0.5 = 1.118033989

Reorder the terms:
0.5 + x3 = 1.118033989

Solving
0.5 + x3 = 1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x3 = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x3 = 1.118033989 + -0.5
x3 = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
x3 = 0.618033989

Simplifying
x3 = 0.618033989

Reorder the terms:
-0.618033989 + x3 = 0.618033989 + -0.618033989

Combine like terms: 0.618033989 + -0.618033989 = 0.000000000
-0.618033989 + 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 + 0.5 = -1.118033989

Simplifying
x3 + 0.5 = -1.118033989

Reorder the terms:
0.5 + x3 = -1.118033989

Solving
0.5 + x3 = -1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x3 = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x3 = -1.118033989 + -0.5
x3 = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
x3 = -1.618033989

Simplifying
x3 = -1.618033989

Reorder the terms:
1.618033989 + x3 = -1.618033989 + 1.618033989

Combine like terms: -1.618033989 + 1.618033989 = 0.000000000
1.618033989 + 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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