6n^4+n^2-10=0

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Solution for 6n^4+n^2-10=0 equation: 


Simplifying
6n4 + n2 + -10 = 0

Reorder the terms:
-10 + n2 + 6n4 = 0

Solving
-10 + n2 + 6n4 = 0

Solving for variable 'n'.

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

Divide each side by '6'.
-1.666666667 + 0.1666666667n2 + n4 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.1666666667n2 + 1.666666667 + n4 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.1666666667n2 + n4 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.1666666667n2 + n4 = 0 + 1.666666667
0.1666666667n2 + n4 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.1666666667n2 + n4 = 1.666666667

The n term is n2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667n2 + 0.25 + n4 = 1.666666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667n2 + n4 = 1.666666667 + 0.25

Combine like terms: 1.666666667 + 0.25 = 1.916666667
0.25 + 0.1666666667n2 + n4 = 1.916666667

Factor a perfect square on the left side:
(n2 + 0.5)(n2 + 0.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(n2 + 0.5) equal to 1.384437311 and -1.384437311.


Subproblem 1
n2 + 0.5 = 1.384437311

Simplifying
n2 + 0.5 = 1.384437311

Reorder the terms:
0.5 + n2 = 1.384437311

Solving
0.5 + n2 = 1.384437311

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n2 = 1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n2 = 1.384437311 + -0.5
n2 = 1.384437311 + -0.5

Combine like terms: 1.384437311 + -0.5 = 0.884437311
n2 = 0.884437311

Simplifying
n2 = 0.884437311

Take the square root of each side:
n = {-0.940445273, 0.940445273}


Subproblem 2
n2 + 0.5 = -1.384437311

Simplifying
n2 + 0.5 = -1.384437311

Reorder the terms:
0.5 + n2 = -1.384437311

Solving
0.5 + n2 = -1.384437311

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n2 = -1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n2 = -1.384437311 + -0.5
n2 = -1.384437311 + -0.5

Combine like terms: -1.384437311 + -0.5 = -1.884437311
n2 = -1.884437311

Simplifying
n2 = -1.884437311

Reorder the terms:
1.884437311 + n2 = -1.884437311 + 1.884437311

Combine like terms: -1.884437311 + 1.884437311 = 0.000000000
1.884437311 + n2 = 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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