solve x2 + 6x + 7 = 0
a) x = -1 and x = -5
b) 3 + - root 2
c) x2 + - root 2
d) (-3 + - root 2)/2

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.

Your maths is very weak try yourself this would improve your skills don't depend on others