x^10-0.75x^5-1=0

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Solution for x^10-0.75x^5-1=0 equation: 


Simplifying
x10 + -0.75x5 + -1 = 0

Reorder the terms:
-1 + -0.75x5 + x10 = 0

Solving
-1 + -0.75x5 + x10 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.75x5 + 1 + x10 = 0 + 1

Reorder the terms:
-1 + 1 + -0.75x5 + x10 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.75x5 + x10 = 0 + 1
-0.75x5 + x10 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.75x5 + x10 = 1

The x term is -0.75x5.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x5 + 0.140625 + x10 = 1 + 0.140625

Reorder the terms:
0.140625 + -0.75x5 + x10 = 1 + 0.140625

Combine like terms: 1 + 0.140625 = 1.140625
0.140625 + -0.75x5 + x10 = 1.140625

Factor a perfect square on the left side:
(x5 + -0.375)(x5 + -0.375) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x5 + -0.375) equal to 1.068000468 and -1.068000468.


Subproblem 1
x5 + -0.375 = 1.068000468

Simplifying
x5 + -0.375 = 1.068000468

Reorder the terms:
-0.375 + x5 = 1.068000468

Solving
-0.375 + x5 = 1.068000468

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x5 = 1.068000468 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x5 = 1.068000468 + 0.375
x5 = 1.068000468 + 0.375

Combine like terms: 1.068000468 + 0.375 = 1.443000468
x5 = 1.443000468

Simplifying
x5 = 1.443000468

Reorder the terms:
-1.443000468 + x5 = 1.443000468 + -1.443000468

Combine like terms: 1.443000468 + -1.443000468 = 0.000000000
-1.443000468 + 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 + -0.375 = -1.068000468

Simplifying
x5 + -0.375 = -1.068000468

Reorder the terms:
-0.375 + x5 = -1.068000468

Solving
-0.375 + x5 = -1.068000468

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x5 = -1.068000468 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x5 = -1.068000468 + 0.375
x5 = -1.068000468 + 0.375

Combine like terms: -1.068000468 + 0.375 = -0.693000468
x5 = -0.693000468

Simplifying
x5 = -0.693000468

Reorder the terms:
0.693000468 + x5 = -0.693000468 + 0.693000468

Combine like terms: -0.693000468 + 0.693000468 = 0.000000000
0.693000468 + 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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