  We use a recently developed method to determine approximate expression for
tritronqu\'{e}e solution for P-1: $y^{\prime \prime} + 6 y^2 - x=0$ in a domain
$D$ with rigorous bounds. In particular we rigorously confirm the location of
the closest singularity from the origin to be at $x= - \frac{770766}{323285} =
-2.3841687675\cdots$ to within $5 \times 10^{-6}$ accuracy, in agreement with
previous numerical calculation.
