What are the solutions to x² + 6x - 7 = 0?

Factor $x^2+6x-7$ by finding two numbers that multiply to $-7$ and add to $6$: those are $7$ and $-1$. So $(x+7)(x-1)=0$, giving $x=-7$ or $x=1$, choice D. The quadratic formula agrees: the discriminant is $36+28=64$, so $x=\frac{-6\pm8}{2}$, which is $1$ or $-7$. Choice A ($-1,-7$) has the correct $-7$ but the wrong second root. Choice B ($-1,7$) reverses the signs of both roots. Choice C ($1,7$) gives the right $1$ and the wrong sign on $7$. Check $x=-7$: $49-42-7=0$.