Question 172938
{{{sqrt (10 + x) = -1 - sqrt (11 - 5x)}}}


Square both sides:


{{{10+x=1+2sqrt(11-5x)+11-5x}}}


Collect like terms:


{{{-2+6x=2sqrt(11-5x)}}}


Square both sides again:


{{{4-24x-36x^2=4(11-5x)}}}


Collect like terms and put into standard form:


{{{36x^2-24x-40=0}}}


Solve the quadratic:


In fact, this horror actually factors {{{(36x-40)(x+1)=0}}}.   So {{{x=10/9}}} or {{{x=-1}}}


Well, that was tidy.  But there is a big problem.  Neither one of the roots calculated actually satisfies the original equation -- try it for yourself.  This makes sense because how could the positive square root on the left be equal to a clearly negative number on the right?  What happened is that the process of squaring the variable (twice in this case) introduced extraneous roots.  There is no solution to this equation.