What is m is 1/m^2 = 1/m - 1/2

Given the equation 1/m^2 = 1/m -
1/2.

We need to find the values of m that satisfies the
equation.

Let us get rid of the denominator by multiplying
by 2m^2.

==> 2m^2(1/m^2) = 2m^2(1/m) -
2m^2(1/2)

==> 2 = 2m -
m^2

Now we will combine all terms on the left
side.

==> m^2 - 2m + 2 =
0.

Now we will use the formula to solve for
m.

==> m1= ( 2 + sqrt(4-8) /
2

             =
(2+sqrt-4)/2

              = (2 +
2i)/2

                 = 1+
i

==> m2= 1-i

Then
there are no real solution for
m.

However, the equation has a complex
solution.

==> m = { 1+i,
1-i}