x^6+9x^3-4=0

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Solution for x^6+9x^3-4=0 equation:


Simplifying
x6 + 9x3 + -4 = 0

Reorder the terms:
-4 + 9x3 + x6 = 0

Solving
-4 + 9x3 + 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 + 9x3 + 4 + x6 = 0 + 4

Reorder the terms:
-4 + 4 + 9x3 + x6 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 9x3 + x6 = 0 + 4
9x3 + x6 = 0 + 4

Combine like terms: 0 + 4 = 4
9x3 + x6 = 4

The x term is 9x3.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x3 + 20.25 + x6 = 4 + 20.25

Reorder the terms:
20.25 + 9x3 + x6 = 4 + 20.25

Combine like terms: 4 + 20.25 = 24.25
20.25 + 9x3 + x6 = 24.25

Factor a perfect square on the left side:
(x3 + 4.5)(x3 + 4.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x3 + 4.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

x3 + 4.5 = 4.924428901 Simplifying x3 + 4.5 = 4.924428901 Reorder the terms: 4.5 + x3 = 4.924428901 Solving 4.5 + x3 = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x3 = 4.924428901 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x3 = 4.924428901 + -4.5 x3 = 4.924428901 + -4.5 Combine like terms: 4.924428901 + -4.5 = 0.424428901 x3 = 0.424428901 Simplifying x3 = 0.424428901 Reorder the terms: -0.424428901 + x3 = 0.424428901 + -0.424428901 Combine like terms: 0.424428901 + -0.424428901 = 0.000000000 -0.424428901 + 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 + 4.5 = -4.924428901 Simplifying x3 + 4.5 = -4.924428901 Reorder the terms: 4.5 + x3 = -4.924428901 Solving 4.5 + x3 = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x3 = -4.924428901 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x3 = -4.924428901 + -4.5 x3 = -4.924428901 + -4.5 Combine like terms: -4.924428901 + -4.5 = -9.424428901 x3 = -9.424428901 Simplifying x3 = -9.424428901 Reorder the terms: 9.424428901 + x3 = -9.424428901 + 9.424428901 Combine like terms: -9.424428901 + 9.424428901 = 0.000000000 9.424428901 + 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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