n^4+n^2-841=0

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Solution for n^4+n^2-841=0 equation: 


Simplifying
n4 + n2 + -841 = 0

Reorder the terms:
-841 + n2 + n4 = 0

Solving
-841 + n2 + n4 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '841' to each side of the equation.
-841 + n2 + 841 + n4 = 0 + 841

Reorder the terms:
-841 + 841 + n2 + n4 = 0 + 841

Combine like terms: -841 + 841 = 0
0 + n2 + n4 = 0 + 841
n2 + n4 = 0 + 841

Combine like terms: 0 + 841 = 841
n2 + n4 = 841

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.
n2 + 0.25 + n4 = 841 + 0.25

Reorder the terms:
0.25 + n2 + n4 = 841 + 0.25

Combine like terms: 841 + 0.25 = 841.25
0.25 + n2 + n4 = 841.25

Factor a perfect square on the left side:
(n2 + 0.5)(n2 + 0.5) = 841.25

Calculate the square root of the right side: 29.004310025

Break this problem into two subproblems by setting 
(n2 + 0.5) equal to 29.004310025 and -29.004310025.


Subproblem 1
n2 + 0.5 = 29.004310025

Simplifying
n2 + 0.5 = 29.004310025

Reorder the terms:
0.5 + n2 = 29.004310025

Solving
0.5 + n2 = 29.004310025

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 = 29.004310025 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n2 = 29.004310025 + -0.5
n2 = 29.004310025 + -0.5

Combine like terms: 29.004310025 + -0.5 = 28.504310025
n2 = 28.504310025

Simplifying
n2 = 28.504310025

Take the square root of each side:
n = {-5.338942782, 5.338942782}


Subproblem 2
n2 + 0.5 = -29.004310025

Simplifying
n2 + 0.5 = -29.004310025

Reorder the terms:
0.5 + n2 = -29.004310025

Solving
0.5 + n2 = -29.004310025

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 = -29.004310025 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n2 = -29.004310025 + -0.5
n2 = -29.004310025 + -0.5

Combine like terms: -29.004310025 + -0.5 = -29.504310025
n2 = -29.504310025

Simplifying
n2 = -29.504310025

Reorder the terms:
29.504310025 + n2 = -29.504310025 + 29.504310025

Combine like terms: -29.504310025 + 29.504310025 = 0.000000000
29.504310025 + 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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