mass - Spontaneous Symmetry Breaking

In Spontaneous symmetry breaking we have got that, a field

$$\phi= \pm \sqrt{\frac{-m^2}{\lambda}}.$$ Now in order to get the unstable minima we need to guess the mass $m^2 <0$. But can mass be negative? Why are we guessing so?

One more question is that, how this lead us to the solution of nonlinear equation?