-x^10-7x^5+4=0

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Solution for -x^10-7x^5+4=0 equation: 


Simplifying
-1x10 + -7x5 + 4 = 0

Reorder the terms:
4 + -7x5 + -1x10 = 0

Solving
4 + -7x5 + -1x10 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 7x5 + x10 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 7x5 + 4 + x10 = 0 + 4

Reorder the terms:
-4 + 4 + 7x5 + x10 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 7x5 + x10 = 0 + 4
7x5 + x10 = 0 + 4

Combine like terms: 0 + 4 = 4
7x5 + x10 = 4

The x term is 7x5.  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.
7x5 + 12.25 + x10 = 4 + 12.25

Reorder the terms:
12.25 + 7x5 + x10 = 4 + 12.25

Combine like terms: 4 + 12.25 = 16.25
12.25 + 7x5 + x10 = 16.25

Factor a perfect square on the left side:
(x5 + 3.5)(x5 + 3.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x5 + 3.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
x5 + 3.5 = 4.031128874

Simplifying
x5 + 3.5 = 4.031128874

Reorder the terms:
3.5 + x5 = 4.031128874

Solving
3.5 + x5 = 4.031128874

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 + x5 = 4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x5 = 4.031128874 + -3.5
x5 = 4.031128874 + -3.5

Combine like terms: 4.031128874 + -3.5 = 0.531128874
x5 = 0.531128874

Simplifying
x5 = 0.531128874

Reorder the terms:
-0.531128874 + x5 = 0.531128874 + -0.531128874

Combine like terms: 0.531128874 + -0.531128874 = 0.000000000
-0.531128874 + 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 + 3.5 = -4.031128874

Simplifying
x5 + 3.5 = -4.031128874

Reorder the terms:
3.5 + x5 = -4.031128874

Solving
3.5 + x5 = -4.031128874

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 + x5 = -4.031128874 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x5 = -4.031128874 + -3.5
x5 = -4.031128874 + -3.5

Combine like terms: -4.031128874 + -3.5 = -7.531128874
x5 = -7.531128874

Simplifying
x5 = -7.531128874

Reorder the terms:
7.531128874 + x5 = -7.531128874 + 7.531128874

Combine like terms: -7.531128874 + 7.531128874 = 0.000000000
7.531128874 + 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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