I begin with $\displaystyle x^2+8x=-15$. Since they say to solve by completing the square, I ignore that it can be factored as is and add one to each side. Since $\displaystyle (1/2*8)^2=16$. And get $\displaystyle x^2+8x+16=1$ after moving the -15 and adding one to each side.

First off have I done everything correctly? Keep in mind that the problem asks for me to complete the square, which I think I have done.

Secondly is the resulting factored equation just asking me for the square root of one? $\displaystyle (x+4)^2=1$ is the same as $\displaystyle a^2=1$. Since x would be what ever number plus four squared is equal to one.

Just from factoring out the initial equation you can tell the answers are -3 and -5. So something has too be wrong.