Question 979430
{{{p+(1/4)*p^(1/2)+K^2=0}}}
=>  {{{p+K^2=-(1/4)*p^(1/2)}}}
=> {{{4p+4K^2 = -p^(1/2)}}}
Squaring both sides,
{{{16p^2+16K^4+32pk^2 = p}}}
=> {{{16p^2+(32K^2-1)p+16K^4 = 0}}}
For perfect square, Discriminant=0
{{{(32K^2-1)^2-4*16*16K^4 = 0}}}
=>{{{1024K^4-64K^2+1-1024K^4=0}}}
=> {{{K^2= 1/64}}}
=> {{{K=1/8}}}