2m^2-m^4=0.5

Solution for 2m^2-m^4=0.5 equation:

Simplifying
2m2 + -1m4 = 0.5

Solving
2m2 + -1m4 = 0.5

Solving for variable 'm'.

Reorder the terms:
-0.5 + 2m2 + -1m4 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-0.5 + 2m2 + -1m4 = 0.0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
0.5 + -2m2 + m4 = 0.0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2m2 + -0.5 + m4 = 0.0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2m2 + m4 = 0.0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2m2 + m4 = 0.0 + -0.5
-2m2 + m4 = 0.0 + -0.5

Combine like terms: 0.0 + -0.5 = -0.5
-2m2 + m4 = -0.5

The m term is -2m2.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m2 + 1 + m4 = -0.5 + 1

Reorder the terms:
1 + -2m2 + m4 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + -2m2 + m4 = 0.5

Factor a perfect square on the left side:
(m2 + -1)(m2 + -1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(m2 + -1) equal to 0.707106781 and -0.707106781.

Subproblem 1
m2 + -1 = 0.707106781

Simplifying
m2 + -1 = 0.707106781

Reorder the terms:
-1 + m2 = 0.707106781

Solving
-1 + m2 = 0.707106781

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 + 1 + m2 = 0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + m2 = 0.707106781 + 1
m2 = 0.707106781 + 1

Combine like terms: 0.707106781 + 1 = 1.707106781
m2 = 1.707106781

Simplifying
m2 = 1.707106781

Take the square root of each side:
m = {-1.306562965, 1.306562965}

Subproblem 2
m2 + -1 = -0.707106781

Simplifying
m2 + -1 = -0.707106781

Reorder the terms:
-1 + m2 = -0.707106781

Solving
-1 + m2 = -0.707106781

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 + 1 + m2 = -0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + m2 = -0.707106781 + 1
m2 = -0.707106781 + 1

Combine like terms: -0.707106781 + 1 = 0.292893219
m2 = 0.292893219

Simplifying
m2 = 0.292893219

Take the square root of each side:
m = {-0.5411961, 0.5411961}

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {-1.306562965, 1.306562965, -0.5411961, 0.5411961}