One way to look at this is to consider a ratio r which when multiplied by, say, the lower number -196 gives the geometric mean m, such that mr=-12, the higher number. So we have m=-196r and mr=-12. Substituting for m we get -196r²=-12, r²=12/196=3/49, r=√3/7 and m=-196√3/7=-48.4974 approx. Now divide by 3: -48.4974/3=-16.1658. The geometric mean is the geometric centre of the two numbers.