2m^4-22m^2=-56

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Solution for 2m^4-22m^2=-56 equation: 


Simplifying
2m4 + -22m2 = -56

Reorder the terms:
-22m2 + 2m4 = -56

Solving
-22m2 + 2m4 = -56

Solving for variable 'm'.

Reorder the terms:
56 + -22m2 + 2m4 = -56 + 56

Combine like terms: -56 + 56 = 0
56 + -22m2 + 2m4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -11m2 + m4) = 0

Factor a trinomial.
2((4 + -1m2)(7 + -1m2)) = 0

Factor a difference between two squares.
2(((2 + m)(2 + -1m))(7 + -1m2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -1m2)' equal to zero and attempt to solve:

Simplifying
7 + -1m2 = 0

Solving
7 + -1m2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1m2 = 0 + -7
-1m2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1m2 = -7

Divide each side by '-1'.
m2 = 7

Simplifying
m2 = 7

Take the square root of each side:
m = {-2.645751311, 2.645751311}

Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 0

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

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

Combine like terms: 2 + -2 = 0
0 + m = 0 + -2
m = 0 + -2

Combine like terms: 0 + -2 = -2
m = -2

Simplifying
m = -2

Subproblem 3
Set the factor '(2 + -1m)' equal to zero and attempt to solve:

Simplifying
2 + -1m = 0

Solving
2 + -1m = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -1m = 0 + -2
-1m = 0 + -2

Combine like terms: 0 + -2 = -2
-1m = -2

Divide each side by '-1'.
m = 2

Simplifying
m = 2
Solution
m = {-2.645751311, 2.645751311, -2, 2}

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