8x^6+x^3-45=0

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Solution for 8x^6+x^3-45=0 equation: 


Simplifying
8x6 + x3 + -45 = 0

Reorder the terms:
-45 + x3 + 8x6 = 0

Solving
-45 + x3 + 8x6 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-5.625 + 0.125x3 + x6 = 0

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + 0.125x3 + 5.625 + x6 = 0 + 5.625

Reorder the terms:
-5.625 + 5.625 + 0.125x3 + x6 = 0 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + 0.125x3 + x6 = 0 + 5.625
0.125x3 + x6 = 0 + 5.625

Combine like terms: 0 + 5.625 = 5.625
0.125x3 + x6 = 5.625

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.
0.125x3 + 0.25 + x6 = 5.625 + 0.25

Reorder the terms:
0.25 + 0.125x3 + x6 = 5.625 + 0.25

Combine like terms: 5.625 + 0.25 = 5.875
0.25 + 0.125x3 + x6 = 5.875

Factor a perfect square on the left side:
(x3 + 0.5)(x3 + 0.5) = 5.875

Calculate the square root of the right side: 2.423839929

Break this problem into two subproblems by setting 
(x3 + 0.5) equal to 2.423839929 and -2.423839929.


Subproblem 1
x3 + 0.5 = 2.423839929

Simplifying
x3 + 0.5 = 2.423839929

Reorder the terms:
0.5 + x3 = 2.423839929

Solving
0.5 + x3 = 2.423839929

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 = 2.423839929 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x3 = 2.423839929 + -0.5
x3 = 2.423839929 + -0.5

Combine like terms: 2.423839929 + -0.5 = 1.923839929
x3 = 1.923839929

Simplifying
x3 = 1.923839929

Reorder the terms:
-1.923839929 + x3 = 1.923839929 + -1.923839929

Combine like terms: 1.923839929 + -1.923839929 = 0.000000000
-1.923839929 + 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 = -2.423839929

Simplifying
x3 + 0.5 = -2.423839929

Reorder the terms:
0.5 + x3 = -2.423839929

Solving
0.5 + x3 = -2.423839929

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 = -2.423839929 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x3 = -2.423839929 + -0.5
x3 = -2.423839929 + -0.5

Combine like terms: -2.423839929 + -0.5 = -2.923839929
x3 = -2.923839929

Simplifying
x3 = -2.923839929

Reorder the terms:
2.923839929 + x3 = -2.923839929 + 2.923839929

Combine like terms: -2.923839929 + 2.923839929 = 0.000000000
2.923839929 + 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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