x^2 + 6x + 3 = 0 .... move the 3 to the other side, be sure and change the sign.
x^2 + 6x = -3 .. take half of x term coefficient, square it, then add to both sides.
x^2 + 6x + 9 = -3 + 9
x^2 + 6x + 9 = 6
(x + 3)^2 = 6
x + 3 = (+,-) sq rt 6
x = (sq rt 6) + 3 and x = (sq rt 6) - 3