Algebra

Equate the two functions to get x^2 = m*x - 2   or  x^2 - m*x + 2 = 0

 

This quadratic has a single point solution if (-m)^2 - 4*1*2 = 0  or m^2 = 8  

 

Therefore there are two possibilities:  m = sqrt(8) and m = -sqrt(8)

 

These mean that the linear function represents tangent lines to the x^2 function.