$AgCl \rightleftharpoons A{g^ + } + C{l^ - }$

i.e., ${K_{sp(AgCl)}} = x \times x$

$KCl \to {K^ + } + \mathop {C{l^ - }}\limits_{0.1} $

$[C{l^ - }]\,$ from $KCl = 0.1\,m$

Total $[C{l^ - }]$ in solution $ = x + 0.1$

${K_{sp}}(AgCl) = [A{g^ + }][C{l^ - }] = x(x + 0.1)$

$1.0 \times {10^{ - 10}} = x(x + 0.1)$

$1.0 \times {10^{ - 10}} = {x^2} + 0.1x$

$1.0 \times {10^{ - 10}} = 0.1x$      (as ${x^2} <  < 1$)

$x = 1.0 \times {10^{ - 9}}\,mol/L$