m^4+24m^2+9=0

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Solution for m^4+24m^2+9=0 equation: 


Simplifying
m4 + 24m2 + 9 = 0

Reorder the terms:
9 + 24m2 + m4 = 0

Solving
9 + 24m2 + m4 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 24m2 + -9 + m4 = 0 + -9

Reorder the terms:
9 + -9 + 24m2 + m4 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 24m2 + m4 = 0 + -9
24m2 + m4 = 0 + -9

Combine like terms: 0 + -9 = -9
24m2 + m4 = -9

The m term is 24m2.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24m2 + 144 + m4 = -9 + 144

Reorder the terms:
144 + 24m2 + m4 = -9 + 144

Combine like terms: -9 + 144 = 135
144 + 24m2 + m4 = 135

Factor a perfect square on the left side:
(m2 + 12)(m2 + 12) = 135

Calculate the square root of the right side: 11.618950039

Break this problem into two subproblems by setting 
(m2 + 12) equal to 11.618950039 and -11.618950039.


Subproblem 1
m2 + 12 = 11.618950039

Simplifying
m2 + 12 = 11.618950039

Reorder the terms:
12 + m2 = 11.618950039

Solving
12 + m2 = 11.618950039

Solving for variable 'm'.

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

Add '-12' to each side of the equation.
12 + -12 + m2 = 11.618950039 + -12

Combine like terms: 12 + -12 = 0
0 + m2 = 11.618950039 + -12
m2 = 11.618950039 + -12

Combine like terms: 11.618950039 + -12 = -0.381049961
m2 = -0.381049961

Simplifying
m2 = -0.381049961

Reorder the terms:
0.381049961 + m2 = -0.381049961 + 0.381049961

Combine like terms: -0.381049961 + 0.381049961 = 0.000000000
0.381049961 + m2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.


Subproblem 2
m2 + 12 = -11.618950039

Simplifying
m2 + 12 = -11.618950039

Reorder the terms:
12 + m2 = -11.618950039

Solving
12 + m2 = -11.618950039

Solving for variable 'm'.

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

Add '-12' to each side of the equation.
12 + -12 + m2 = -11.618950039 + -12

Combine like terms: 12 + -12 = 0
0 + m2 = -11.618950039 + -12
m2 = -11.618950039 + -12

Combine like terms: -11.618950039 + -12 = -23.618950039
m2 = -23.618950039

Simplifying
m2 = -23.618950039

Reorder the terms:
23.618950039 + m2 = -23.618950039 + 23.618950039

Combine like terms: -23.618950039 + 23.618950039 = 0.000000000
23.618950039 + 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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