A man lived in the 19th century and said " I was x years old when in the year x^2. In what year he was born

Question

August De Morgan lived in the nineteenth century. He made the statement : I was x years old when in the year x^2." In what year was he born?

Answer 1

√1801 ≤ x ≤ √1899

42.438 ≤ x ≤ 43.578 

 

How old is he and when was he born?