Let a = (v2 + u2)/2, b = u*v, c = (v2 - u2)/2, then
a*(1 + x2) + 2bx + c*(1 - x2) = (1 + x2)(v2 + u2)/2 + 2uvx + (1-x2)(v2 - u2)/2 = (ux + v)2
Choose whatever numbers you like for u and v.
For example, if u = 3 and v = 5
a = 17, b = 15, c = -8 and 17*(1 + x2) + 2*30*x - 8*(1 - x2) = 25x2 + 30x + 9 = (5x + 3)2
.