X^10-33X^5-32=0

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Solution for X^10-33X^5-32=0 equation: 


Simplifying
X10 + -33X5 + -32 = 0

Reorder the terms:
-32 + -33X5 + X10 = 0

Solving
-32 + -33X5 + X10 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -33X5 + 32 + X10 = 0 + 32

Reorder the terms:
-32 + 32 + -33X5 + X10 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -33X5 + X10 = 0 + 32
-33X5 + X10 = 0 + 32

Combine like terms: 0 + 32 = 32
-33X5 + X10 = 32

The X term is -33X5.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33X5 + 272.25 + X10 = 32 + 272.25

Reorder the terms:
272.25 + -33X5 + X10 = 32 + 272.25

Combine like terms: 32 + 272.25 = 304.25
272.25 + -33X5 + X10 = 304.25

Factor a perfect square on the left side:
(X5 + -16.5)(X5 + -16.5) = 304.25

Calculate the square root of the right side: 17.442763543

Break this problem into two subproblems by setting 
(X5 + -16.5) equal to 17.442763543 and -17.442763543.


Subproblem 1
X5 + -16.5 = 17.442763543

Simplifying
X5 + -16.5 = 17.442763543

Reorder the terms:
-16.5 + X5 = 17.442763543

Solving
-16.5 + X5 = 17.442763543

Solving for variable 'X'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + X5 = 17.442763543 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + X5 = 17.442763543 + 16.5
X5 = 17.442763543 + 16.5

Combine like terms: 17.442763543 + 16.5 = 33.942763543
X5 = 33.942763543

Simplifying
X5 = 33.942763543

Reorder the terms:
-33.942763543 + X5 = 33.942763543 + -33.942763543

Combine like terms: 33.942763543 + -33.942763543 = 0.000000000
-33.942763543 + X5 = 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
X5 + -16.5 = -17.442763543

Simplifying
X5 + -16.5 = -17.442763543

Reorder the terms:
-16.5 + X5 = -17.442763543

Solving
-16.5 + X5 = -17.442763543

Solving for variable 'X'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + X5 = -17.442763543 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + X5 = -17.442763543 + 16.5
X5 = -17.442763543 + 16.5

Combine like terms: -17.442763543 + 16.5 = -0.942763543
X5 = -0.942763543

Simplifying
X5 = -0.942763543

Reorder the terms:
0.942763543 + X5 = -0.942763543 + 0.942763543

Combine like terms: -0.942763543 + 0.942763543 = 0.000000000
0.942763543 + X5 = 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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