m^4+18m^2+18=0

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Solution for m^4+18m^2+18=0 equation: 


Simplifying
m4 + 18m2 + 18 = 0

Reorder the terms:
18 + 18m2 + m4 = 0

Solving
18 + 18m2 + m4 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 18m2 + -18 + m4 = 0 + -18

Reorder the terms:
18 + -18 + 18m2 + m4 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 18m2 + m4 = 0 + -18
18m2 + m4 = 0 + -18

Combine like terms: 0 + -18 = -18
18m2 + m4 = -18

The m term is 18m2.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18m2 + 81 + m4 = -18 + 81

Reorder the terms:
81 + 18m2 + m4 = -18 + 81

Combine like terms: -18 + 81 = 63
81 + 18m2 + m4 = 63

Factor a perfect square on the left side:
(m2 + 9)(m2 + 9) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(m2 + 9) equal to 7.937253933 and -7.937253933.


Subproblem 1
m2 + 9 = 7.937253933

Simplifying
m2 + 9 = 7.937253933

Reorder the terms:
9 + m2 = 7.937253933

Solving
9 + m2 = 7.937253933

Solving for variable 'm'.

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

Add '-9' to each side of the equation.
9 + -9 + m2 = 7.937253933 + -9

Combine like terms: 9 + -9 = 0
0 + m2 = 7.937253933 + -9
m2 = 7.937253933 + -9

Combine like terms: 7.937253933 + -9 = -1.062746067
m2 = -1.062746067

Simplifying
m2 = -1.062746067

Reorder the terms:
1.062746067 + m2 = -1.062746067 + 1.062746067

Combine like terms: -1.062746067 + 1.062746067 = 0.000000000
1.062746067 + 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 + 9 = -7.937253933

Simplifying
m2 + 9 = -7.937253933

Reorder the terms:
9 + m2 = -7.937253933

Solving
9 + m2 = -7.937253933

Solving for variable 'm'.

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

Add '-9' to each side of the equation.
9 + -9 + m2 = -7.937253933 + -9

Combine like terms: 9 + -9 = 0
0 + m2 = -7.937253933 + -9
m2 = -7.937253933 + -9

Combine like terms: -7.937253933 + -9 = -16.937253933
m2 = -16.937253933

Simplifying
m2 = -16.937253933

Reorder the terms:
16.937253933 + m2 = -16.937253933 + 16.937253933

Combine like terms: -16.937253933 + 16.937253933 = 0.000000000
16.937253933 + 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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