x^6-1262x^3=-125

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Solution for x^6-1262x^3=-125 equation: 


Simplifying
x6 + -1262x3 = -125

Reorder the terms:
-1262x3 + x6 = -125

Solving
-1262x3 + x6 = -125

Solving for variable 'x'.

Reorder the terms:
125 + -1262x3 + x6 = -125 + 125

Combine like terms: -125 + 125 = 0
125 + -1262x3 + x6 = 0

Begin completing the square.

Move the constant term to the right:

Add '-125' to each side of the equation.
125 + -1262x3 + -125 + x6 = 0 + -125

Reorder the terms:
125 + -125 + -1262x3 + x6 = 0 + -125

Combine like terms: 125 + -125 = 0
0 + -1262x3 + x6 = 0 + -125
-1262x3 + x6 = 0 + -125

Combine like terms: 0 + -125 = -125
-1262x3 + x6 = -125

The x term is -1262x3.  Take half its coefficient (-631).
Square it (398161) and add it to both sides.

Add '398161' to each side of the equation.
-1262x3 + 398161 + x6 = -125 + 398161

Reorder the terms:
398161 + -1262x3 + x6 = -125 + 398161

Combine like terms: -125 + 398161 = 398036
398161 + -1262x3 + x6 = 398036

Factor a perfect square on the left side:
(x3 + -631)(x3 + -631) = 398036

Calculate the square root of the right side: 630.900943096

Break this problem into two subproblems by setting 
(x3 + -631) equal to 630.900943096 and -630.900943096.


Subproblem 1
x3 + -631 = 630.900943096

Simplifying
x3 + -631 = 630.900943096

Reorder the terms:
-631 + x3 = 630.900943096

Solving
-631 + x3 = 630.900943096

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '631' to each side of the equation.
-631 + 631 + x3 = 630.900943096 + 631

Combine like terms: -631 + 631 = 0
0 + x3 = 630.900943096 + 631
x3 = 630.900943096 + 631

Combine like terms: 630.900943096 + 631 = 1261.900943096
x3 = 1261.900943096

Simplifying
x3 = 1261.900943096

Reorder the terms:
-1261.900943096 + x3 = 1261.900943096 + -1261.900943096

Combine like terms: 1261.900943096 + -1261.900943096 = 0.000000000
-1261.900943096 + 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 + -631 = -630.900943096

Simplifying
x3 + -631 = -630.900943096

Reorder the terms:
-631 + x3 = -630.900943096

Solving
-631 + x3 = -630.900943096

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '631' to each side of the equation.
-631 + 631 + x3 = -630.900943096 + 631

Combine like terms: -631 + 631 = 0
0 + x3 = -630.900943096 + 631
x3 = -630.900943096 + 631

Combine like terms: -630.900943096 + 631 = 0.099056904
x3 = 0.099056904

Simplifying
x3 = 0.099056904

Reorder the terms:
-0.099056904 + x3 = 0.099056904 + -0.099056904

Combine like terms: 0.099056904 + -0.099056904 = 0.000000000
-0.099056904 + 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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