A student performed the following steps to find the solution to the equation x^2+14x+40=0 where did the student go wrong

2 answers:

7 0

I don't fully know exactly what your asking and I'm new at this, but I think you're asking about what is the center and radius of a circle right? In that case, this is what I came up with (Don't know if this is what you want, sorry) :(
First step: You do -40 to the current +40, and transfer it to the other side of the equal symbol, making the 0 turn into a -40.
Second step: It should now look like this - (x^2+14x) = -40
Third step: Divide the 14 by 2, which gives you a positive 7, then square that 7, which gives you 49. It shall look like this now - (x^2+14x+49) = 9. The nine is now there at the end because you add the 49 to the negative 40.
Fourth step: Remember the 7? Well, we use it now. It should currently look like this - (x+7) = 9.
Fifth step: The Center can now be found, and remember for the center you do the opposite of what the number is, in this case, the positive 7, will be a negative 7 in the center. Since there is no y found, it will remain as 0. (I think) This is how It looks - Center: (-7, 0)
Sixth step (Final step): Now the radius must be found, we will now look at the nine at the other side of the equal symbol. We square root that now! So the radius = 3.
Answers: Center: (-7, 0) Radius: 3. (Or if asked to find diameter, then it would be double the 3. Meaning Diameter=6.
Comment: I'm only a 9th grader, so sorry If I got this wrong. Trying to help :p lol.