1954 AHSME Problem 44

A man born in the first half of the nineteenth century was x years old in the year x^2. He was born in:

\textbf{(A)}\ 1849 \qquad \textbf{(B)}\ 1825 \qquad \textbf{(C)}\ 1812 \qquad \textbf{(D)}\ 1836 \qquad \textbf{(E)}\ 1806

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.