x^6+7x^3-10=0

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Solution for x^6+7x^3-10=0 equation:


Simplifying
x6 + 7x3 + -10 = 0

Reorder the terms:
-10 + 7x3 + x6 = 0

Solving
-10 + 7x3 + x6 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 7x3 + 10 + x6 = 0 + 10

Reorder the terms:
-10 + 10 + 7x3 + x6 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 7x3 + x6 = 0 + 10
7x3 + x6 = 0 + 10

Combine like terms: 0 + 10 = 10
7x3 + x6 = 10

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 = 10 + 12.25

Reorder the terms:
12.25 + 7x3 + x6 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + 7x3 + x6 = 22.25

Factor a perfect square on the left side:
(x3 + 3.5)(x3 + 3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x3 + 3.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

x3 + 3.5 = 4.716990566 Simplifying x3 + 3.5 = 4.716990566 Reorder the terms: 3.5 + x3 = 4.716990566 Solving 3.5 + x3 = 4.716990566 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 = 4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x3 = 4.716990566 + -3.5 x3 = 4.716990566 + -3.5 Combine like terms: 4.716990566 + -3.5 = 1.216990566 x3 = 1.216990566 Simplifying x3 = 1.216990566 Reorder the terms: -1.216990566 + x3 = 1.216990566 + -1.216990566 Combine like terms: 1.216990566 + -1.216990566 = 0.000000000 -1.216990566 + 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 = -4.716990566 Simplifying x3 + 3.5 = -4.716990566 Reorder the terms: 3.5 + x3 = -4.716990566 Solving 3.5 + x3 = -4.716990566 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 = -4.716990566 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x3 = -4.716990566 + -3.5 x3 = -4.716990566 + -3.5 Combine like terms: -4.716990566 + -3.5 = -8.216990566 x3 = -8.216990566 Simplifying x3 = -8.216990566 Reorder the terms: 8.216990566 + x3 = -8.216990566 + 8.216990566 Combine like terms: -8.216990566 + 8.216990566 = 0.000000000 8.216990566 + 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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