How can I solve it?? ∫exp(x²)dx=??

Question

My formulas are: y=(x+a)^2 x=(-y+a)^2 I would like to solve for a where they touch (exact solution). Here is a graph demonstrating what I mean: As you can see, I have attempted to solve for a by making them closer and closer. I think 1.100917368760402698 ≤ a ≤ 1.100917368760402699, but floating point error may have reduced the accuracy of that range, but it should be near those numbers at least. There will also be a negative solution of a , which will be exactly negative I believe.

https://youtu.be/FiiZu_V6sUc

Thanks a lot.