7m^2=18-m^4

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Solution for 7m^2=18-m^4 equation: 


Simplifying
7m2 = 18 + -1m4

Solving
7m2 = 18 + -1m4

Solving for variable 'm'.

Reorder the terms:
-18 + 7m2 + m4 = 18 + -1m4 + -18 + m4

Reorder the terms:
-18 + 7m2 + m4 = 18 + -18 + -1m4 + m4

Combine like terms: 18 + -18 = 0
-18 + 7m2 + m4 = 0 + -1m4 + m4
-18 + 7m2 + m4 = -1m4 + m4

Combine like terms: -1m4 + m4 = 0
-18 + 7m2 + m4 = 0

Factor a trinomial.
(-9 + -1m2)(2 + -1m2) = 0


Subproblem 1
Set the factor '(-9 + -1m2)' equal to zero and attempt to solve:

Simplifying
-9 + -1m2 = 0

Solving
-9 + -1m2 = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1m2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1m2 = 0 + 9
-1m2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1m2 = 9

Divide each side by '-1'.
m2 = -9

Simplifying
m2 = -9

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2 + -1m2)' equal to zero and attempt to solve:

Simplifying
2 + -1m2 = 0

Solving
2 + -1m2 = 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 + -1m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m2 = 0 + -2
-1m2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1m2 = -2

Divide each side by '-1'.
m2 = 2

Simplifying
m2 = 2

Take the square root of each side:
m = {-1.414213562, 1.414213562}
Solution
m = {-1.414213562, 1.414213562}

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