M^2+m/2=-1/16

Answer 1

multiply by 16 and you have
16m^2 + 8m + 1 = 0
(4m+1)^2 = 0
m = -1/4

Answer 2

m^2 + m/2 + 1/16 = 0
(m +1/4) (m + 1/4) = 0 ... :) (to complete square take half of middle and square it)
m = -1/4 and -1/4 (just hits the axis )