M^4-2m^2+1=0

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Solution for M^4-2m^2+1=0 equation: 


Simplifying
M4 + -2m2 + 1 = 0

Reorder the terms:
1 + M4 + -2m2 = 0

Solving
1 + M4 + -2m2 = 0

Solving for variable 'M'.

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

Add '-1' to each side of the equation.
1 + M4 + -1 + -2m2 = 0 + -1

Reorder the terms:
1 + -1 + M4 + -2m2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + M4 + -2m2 = 0 + -1
M4 + -2m2 = 0 + -1

Combine like terms: 0 + -1 = -1
M4 + -2m2 = -1

Add '2m2' to each side of the equation.
M4 + -2m2 + 2m2 = -1 + 2m2

Combine like terms: -2m2 + 2m2 = 0
M4 + 0 = -1 + 2m2
M4 = -1 + 2m2

Simplifying
M4 = -1 + 2m2

Reorder the terms:
1 + M4 + -2m2 = -1 + 2m2 + 1 + -2m2

Reorder the terms:
1 + M4 + -2m2 = -1 + 1 + 2m2 + -2m2

Combine like terms: -1 + 1 = 0
1 + M4 + -2m2 = 0 + 2m2 + -2m2
1 + M4 + -2m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
1 + M4 + -2m2 = 0

Factor a trinomial.
(M2 + -1m)(M2 + 2m) = 0


Subproblem 1
Set the factor '(M2 + -1m)' equal to zero and attempt to solve:

Simplifying
M2 + -1m = 0

Solving
M2 + -1m = 0

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

Add 'm' to each side of the equation.
M2 + -1m + m = 0 + m

Combine like terms: -1m + m = 0
M2 + 0 = 0 + m
M2 = 0 + m
Remove the zero:
M2 = m

Simplifying
M2 = m

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 '(M2 + 2m)' equal to zero and attempt to solve:

Simplifying
M2 + 2m = 0

Solving
M2 + 2m = 0

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

Add '-2m' to each side of the equation.
M2 + 2m + -2m = 0 + -2m

Combine like terms: 2m + -2m = 0
M2 + 0 = 0 + -2m
M2 = 0 + -2m
Remove the zero:
M2 = -2m

Simplifying
M2 = -2m

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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