u^4=-2u^2-1

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Solution for u^4=-2u^2-1 equation:


Simplifying
u4 = -2u2 + -1

Reorder the terms:
u4 = -1 + -2u2

Solving
u4 = -1 + -2u2

Solving for variable 'u'.

Reorder the terms:
1 + 2u2 + u4 = -1 + -2u2 + 1 + 2u2

Reorder the terms:
1 + 2u2 + u4 = -1 + 1 + -2u2 + 2u2

Combine like terms: -1 + 1 = 0
1 + 2u2 + u4 = 0 + -2u2 + 2u2
1 + 2u2 + u4 = -2u2 + 2u2

Combine like terms: -2u2 + 2u2 = 0
1 + 2u2 + u4 = 0

Factor a trinomial.
(1 + u2)(1 + u2) = 0

Subproblem 1

Set the factor '(1 + u2)' equal to zero and attempt to solve: Simplifying 1 + u2 = 0 Solving 1 + u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + u2 = 0 + -1 u2 = 0 + -1 Combine like terms: 0 + -1 = -1 u2 = -1 Simplifying u2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + u2)' equal to zero and attempt to solve: Simplifying 1 + u2 = 0 Solving 1 + u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + u2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + u2 = 0 + -1 u2 = 0 + -1 Combine like terms: 0 + -1 = -1 u2 = -1 Simplifying u2 = -1 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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