Question 1019658
For the quadratic equation to have only one solution, the discriminant 
{{{b^2 - 4ac}}} must be equal to 0.
Hence,

{{{64p^2 - 4(1-2p)(-(2+8p)) = 0}}}
<==> {{{64p^2 +8(1-2p)(1+4p) = 0}}}
<==> {{{8p^2 +(1-2p)(1+4p) = 0}}}
<==> {{{8p^2 + 1+4p-2p-8p^2 = 0}}}

==> 1+2p = 0
==> p = -1/2.