This polynomial does not factor so you have to complete the square or use Quadratic formula.
x^2 + 6x + 7 = 0
Using completing the square, subtract 7 from both sides.
x^2 + 6x = -7
divide 6 by 2 = 3, square 3 = 9, add 9 to both sides.
x^2 + 6x + 9 = 2
(x + 3)^2 = 2
Take the sqrt of both sides
x + 3 = + - sqrt 2
subtract 3 from both sides
x = - 3 + - sqrt 2
This is not an answer choice but it is the correct answer. You either typed the choices incorrectly or the equation incorrectly.