
Casey B. answered 03/28/19
Math, Science, and Writing Tutor with ESOL Endorsement
The only reason you may use this in writing is if you want to convey a particular dialect or accent for a character who is speaking. When just writing, you would need to write out wouldn't. In fact, using "would not" would be better than "wouldn't". You want to avoid using contractions when writing formal or professional communications.