First-Order Equations · Superchallenge problem

A curve in the first quadrant starts at $(0,1)$, and along it $y$ decreases as $x$ increases. At every point $P$ of the curve, the segment of the tangent line from $P$ to the $x$-axis has length $1$. Find the $x$-coordinate of the point of the curve where $y=\dfrac12$.