x^6+7x^3-56=0

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Solution for x^6+7x^3-56=0 equation:


Simplifying
x6 + 7x3 + -56 = 0

Reorder the terms:
-56 + 7x3 + x6 = 0

Solving
-56 + 7x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + 7x3 + 56 + x6 = 0 + 56

Reorder the terms:
-56 + 56 + 7x3 + x6 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 7x3 + x6 = 0 + 56
7x3 + x6 = 0 + 56

Combine like terms: 0 + 56 = 56
7x3 + x6 = 56

The x term is 7x3.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x3 + 12.25 + x6 = 56 + 12.25

Reorder the terms:
12.25 + 7x3 + x6 = 56 + 12.25

Combine like terms: 56 + 12.25 = 68.25
12.25 + 7x3 + x6 = 68.25

Factor a perfect square on the left side:
(x3 + 3.5)(x3 + 3.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x3 + 3.5) equal to 8.261355821 and -8.261355821.

Subproblem 1

x3 + 3.5 = 8.261355821 Simplifying x3 + 3.5 = 8.261355821 Reorder the terms: 3.5 + x3 = 8.261355821 Solving 3.5 + x3 = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x3 = 8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x3 = 8.261355821 + -3.5 x3 = 8.261355821 + -3.5 Combine like terms: 8.261355821 + -3.5 = 4.761355821 x3 = 4.761355821 Simplifying x3 = 4.761355821 Reorder the terms: -4.761355821 + x3 = 4.761355821 + -4.761355821 Combine like terms: 4.761355821 + -4.761355821 = 0.000000000 -4.761355821 + 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 + 3.5 = -8.261355821 Simplifying x3 + 3.5 = -8.261355821 Reorder the terms: 3.5 + x3 = -8.261355821 Solving 3.5 + x3 = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x3 = -8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x3 = -8.261355821 + -3.5 x3 = -8.261355821 + -3.5 Combine like terms: -8.261355821 + -3.5 = -11.761355821 x3 = -11.761355821 Simplifying x3 = -11.761355821 Reorder the terms: 11.761355821 + x3 = -11.761355821 + 11.761355821 Combine like terms: -11.761355821 + 11.761355821 = 0.000000000 11.761355821 + 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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