2x^2 + 3y^2 + 8x - 10y + 62
(2x^2 + 8x) + 3y^2 - 10y + 62
(2(x+2)^2 - 8) + (3(y - 5/3)^2 - 25/3) + 62
2(x+2)^2 + 3(y - 5/3)^2 + 45 2/3
Quadratics have to be non-negative, meaning that 2(x+2)^2 and 3(y - 5/3)^2 have the lowest value of 0.
0 + 0 + 45 2/3 = 45 2/3.
=^._.^=
