Question 874864
{{{sqrt(5x+1)-sqrt(x)=5}}}



{{{sqrt(5x+1)=5+sqrt(x)}}}



{{{(sqrt(5x+1))^2=(5+sqrt(x))^2}}}



{{{5x+1=(5+sqrt(x))^2}}}



{{{5x+1=25+10*sqrt(x)+x}}}



{{{5x+1-25-x=10*sqrt(x)}}}



{{{4x-24=10*sqrt(x)}}}



{{{(4x-24)^2=(10*sqrt(x))^2}}}



{{{(4x-24)^2=100x}}}



{{{16x^2-192x+576=100x}}}



{{{16x^2-192x+576-100x=0}}}



{{{16x^2-292x+576=0}}}



{{{4(4x-9)(x-16)=0}}}



{{{4x-9=0}}} or {{{x-16=0}}}



{{{x=9/4}}} or {{{x=16}}}



The *possible* solutions are {{{x=9/4}}} or {{{x=16}}}



However, you'll find that plugging {{{x=9/4}}} back into {{{sqrt(5x+1)-sqrt(x)=5}}} results in a false equation (I'll let you do that part).



Plugging {{{x=16}}} into {{{sqrt(5x+1)-sqrt(x)=5}}} results in a true equation (I'll let you do that part as well).



So that means {{{x=16}}} is the only solution.