150N^8+40N^4-15=0

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Solution for 150N^8+40N^4-15=0 equation: 


Simplifying
150N8 + 40N4 + -15 = 0

Reorder the terms:
-15 + 40N4 + 150N8 = 0

Solving
-15 + 40N4 + 150N8 = 0

Solving for variable 'N'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + 8N4 + 30N8) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-3 + 8N4 + 30N8)' equal to zero and attempt to solve:

Simplifying
-3 + 8N4 + 30N8 = 0

Solving
-3 + 8N4 + 30N8 = 0

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

Divide each side by '30'.
-0.1 + 0.2666666667N4 + N8 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.2666666667N4 + 0.1 + N8 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.2666666667N4 + N8 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.2666666667N4 + N8 = 0.0 + 0.1
0.2666666667N4 + N8 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
0.2666666667N4 + N8 = 0.1

The N term is 0.2666666667N4.  Take half its coefficient (0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
0.2666666667N4 + 0.01777777780 + N8 = 0.1 + 0.01777777780

Reorder the terms:
0.01777777780 + 0.2666666667N4 + N8 = 0.1 + 0.01777777780

Combine like terms: 0.1 + 0.01777777780 = 0.1177777778
0.01777777780 + 0.2666666667N4 + N8 = 0.1177777778

Factor a perfect square on the left side:
(N4 + 0.1333333334)(N4 + 0.1333333334) = 0.1177777778

Calculate the square root of the right side: 0.343187671

Break this problem into two subproblems by setting 
(N4 + 0.1333333334) equal to 0.343187671 and -0.343187671.


Subproblem 1
N4 + 0.1333333334 = 0.343187671

Simplifying
N4 + 0.1333333334 = 0.343187671

Reorder the terms:
0.1333333334 + N4 = 0.343187671

Solving
0.1333333334 + N4 = 0.343187671

Solving for variable 'N'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + N4 = 0.343187671 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + N4 = 0.343187671 + -0.1333333334
N4 = 0.343187671 + -0.1333333334

Combine like terms: 0.343187671 + -0.1333333334 = 0.2098543376
N4 = 0.2098543376

Simplifying
N4 = 0.2098543376

Reorder the terms:
-0.2098543376 + N4 = 0.2098543376 + -0.2098543376

Combine like terms: 0.2098543376 + -0.2098543376 = 0.0000000000
-0.2098543376 + N4 = 0.0000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
N4 + 0.1333333334 = -0.343187671

Simplifying
N4 + 0.1333333334 = -0.343187671

Reorder the terms:
0.1333333334 + N4 = -0.343187671

Solving
0.1333333334 + N4 = -0.343187671

Solving for variable 'N'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + N4 = -0.343187671 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + N4 = -0.343187671 + -0.1333333334
N4 = -0.343187671 + -0.1333333334

Combine like terms: -0.343187671 + -0.1333333334 = -0.4765210044
N4 = -0.4765210044

Simplifying
N4 = -0.4765210044

Reorder the terms:
0.4765210044 + N4 = -0.4765210044 + 0.4765210044

Combine like terms: -0.4765210044 + 0.4765210044 = 0.0000000000
0.4765210044 + N4 = 0.0000000000

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.

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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