m^4+5m^2-3.219=0

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Solution for m^4+5m^2-3.219=0 equation: 


Simplifying
m4 + 5m2 + -3.219 = 0

Reorder the terms:
-3.219 + 5m2 + m4 = 0

Solving
-3.219 + 5m2 + m4 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '3.219' to each side of the equation.
-3.219 + 5m2 + 3.219 + m4 = 0 + 3.219

Reorder the terms:
-3.219 + 3.219 + 5m2 + m4 = 0 + 3.219

Combine like terms: -3.219 + 3.219 = 0.000
0.000 + 5m2 + m4 = 0 + 3.219
5m2 + m4 = 0 + 3.219

Combine like terms: 0 + 3.219 = 3.219
5m2 + m4 = 3.219

The m term is 5m2.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5m2 + 6.25 + m4 = 3.219 + 6.25

Reorder the terms:
6.25 + 5m2 + m4 = 3.219 + 6.25

Combine like terms: 3.219 + 6.25 = 9.469
6.25 + 5m2 + m4 = 9.469

Factor a perfect square on the left side:
(m2 + 2.5)(m2 + 2.5) = 9.469

Calculate the square root of the right side: 3.077174028

Break this problem into two subproblems by setting 
(m2 + 2.5) equal to 3.077174028 and -3.077174028.


Subproblem 1
m2 + 2.5 = 3.077174028

Simplifying
m2 + 2.5 = 3.077174028

Reorder the terms:
2.5 + m2 = 3.077174028

Solving
2.5 + m2 = 3.077174028

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m2 = 3.077174028 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m2 = 3.077174028 + -2.5
m2 = 3.077174028 + -2.5

Combine like terms: 3.077174028 + -2.5 = 0.577174028
m2 = 0.577174028

Simplifying
m2 = 0.577174028

Take the square root of each side:
m = {-0.759719704, 0.759719704}


Subproblem 2
m2 + 2.5 = -3.077174028

Simplifying
m2 + 2.5 = -3.077174028

Reorder the terms:
2.5 + m2 = -3.077174028

Solving
2.5 + m2 = -3.077174028

Solving for variable 'm'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + m2 = -3.077174028 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + m2 = -3.077174028 + -2.5
m2 = -3.077174028 + -2.5

Combine like terms: -3.077174028 + -2.5 = -5.577174028
m2 = -5.577174028

Simplifying
m2 = -5.577174028

Reorder the terms:
5.577174028 + m2 = -5.577174028 + 5.577174028

Combine like terms: -5.577174028 + 5.577174028 = 0.000000000
5.577174028 + m2 = 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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