x^6-28x^3+28=0

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Solution for x^6-28x^3+28=0 equation:


Simplifying
x6 + -28x3 + 28 = 0

Reorder the terms:
28 + -28x3 + x6 = 0

Solving
28 + -28x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -28x3 + -28 + x6 = 0 + -28

Reorder the terms:
28 + -28 + -28x3 + x6 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -28x3 + x6 = 0 + -28
-28x3 + x6 = 0 + -28

Combine like terms: 0 + -28 = -28
-28x3 + x6 = -28

The x term is -28x3.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x3 + 196 + x6 = -28 + 196

Reorder the terms:
196 + -28x3 + x6 = -28 + 196

Combine like terms: -28 + 196 = 168
196 + -28x3 + x6 = 168

Factor a perfect square on the left side:
(x3 + -14)(x3 + -14) = 168

Calculate the square root of the right side: 12.961481397

Break this problem into two subproblems by setting 
(x3 + -14) equal to 12.961481397 and -12.961481397.

Subproblem 1

x3 + -14 = 12.961481397 Simplifying x3 + -14 = 12.961481397 Reorder the terms: -14 + x3 = 12.961481397 Solving -14 + x3 = 12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x3 = 12.961481397 + 14 Combine like terms: -14 + 14 = 0 0 + x3 = 12.961481397 + 14 x3 = 12.961481397 + 14 Combine like terms: 12.961481397 + 14 = 26.961481397 x3 = 26.961481397 Simplifying x3 = 26.961481397 Reorder the terms: -26.961481397 + x3 = 26.961481397 + -26.961481397 Combine like terms: 26.961481397 + -26.961481397 = 0.000000000 -26.961481397 + 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 + -14 = -12.961481397 Simplifying x3 + -14 = -12.961481397 Reorder the terms: -14 + x3 = -12.961481397 Solving -14 + x3 = -12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x3 = -12.961481397 + 14 Combine like terms: -14 + 14 = 0 0 + x3 = -12.961481397 + 14 x3 = -12.961481397 + 14 Combine like terms: -12.961481397 + 14 = 1.038518603 x3 = 1.038518603 Simplifying x3 = 1.038518603 Reorder the terms: -1.038518603 + x3 = 1.038518603 + -1.038518603 Combine like terms: 1.038518603 + -1.038518603 = 0.000000000 -1.038518603 + 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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