The path of a total solar eclipse is modeled by f$($t$)=0\mathrm{.}00372$t$2-0\mathrm{.}493$t $+23\mathrm{.}263,$ where f$($t$)$ is the latitude in degrees south of the equator at t minutes after the start of the total eclipse. What is the latitude closest to the equator, in degrees, at which the total eclipse will be visible? The latitude closest to the equator at which the total eclipse will be visible is $$S$.($Round the final answer to two decimal places as needed. Round all intermediate values to four decimal places as needed.$)$