After a lot of interview rounds and a lengthy process for a tech job I applied, I got a phone call from the recruiter that they'd like to offer me the role.
Over the phone, she asked me they are thinking of offering package of $(X)k/year and asked me what figure had I in my mind. I promptly said without thinking that I have in my mind between $(X + 5)k and $(X + 10)k since I need a job. She promptly said that ok then it'll be $(X + 5)k. I haven't yet got any formal offer letter and this was a phone conversation.
My question is after the recruiter agreeing to the minimum of my specified range, can I negotiate more?
If yes, when should I do it? Once I'm emailed the offer letter?
Also, I was called in to grab some paperwork and one of the papers was the job application form which has a 'desired salary' field. Should I just mention the amount that I want in that field? Also, can I ask anything beyond $(X + 10)k, which is the upper limit of the range that I specified?