x^6+6x^3-5=0

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Solution for x^6+6x^3-5=0 equation:


Simplifying
x6 + 6x3 + -5 = 0

Reorder the terms:
-5 + 6x3 + x6 = 0

Solving
-5 + 6x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6x3 + 5 + x6 = 0 + 5

Reorder the terms:
-5 + 5 + 6x3 + x6 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6x3 + x6 = 0 + 5
6x3 + x6 = 0 + 5

Combine like terms: 0 + 5 = 5
6x3 + x6 = 5

The x term is 6x3.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x3 + 9 + x6 = 5 + 9

Reorder the terms:
9 + 6x3 + x6 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6x3 + x6 = 14

Factor a perfect square on the left side:
(x3 + 3)(x3 + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x3 + 3) equal to 3.741657387 and -3.741657387.

Subproblem 1

x3 + 3 = 3.741657387 Simplifying x3 + 3 = 3.741657387 Reorder the terms: 3 + x3 = 3.741657387 Solving 3 + x3 = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x3 = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x3 = 3.741657387 + -3 x3 = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 x3 = 0.741657387 Simplifying x3 = 0.741657387 Reorder the terms: -0.741657387 + x3 = 0.741657387 + -0.741657387 Combine like terms: 0.741657387 + -0.741657387 = 0.000000000 -0.741657387 + 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 + 3 = -3.741657387 Simplifying x3 + 3 = -3.741657387 Reorder the terms: 3 + x3 = -3.741657387 Solving 3 + x3 = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x3 = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x3 = -3.741657387 + -3 x3 = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 x3 = -6.741657387 Simplifying x3 = -6.741657387 Reorder the terms: 6.741657387 + x3 = -6.741657387 + 6.741657387 Combine like terms: -6.741657387 + 6.741657387 = 0.000000000 6.741657387 + 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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