Question 612920
{{{sqrt(x+10)+sqrt(3-x)=5}}}


{{{sqrt(x+10)=5-sqrt(3-x)}}}


{{{(sqrt(x+10))^2=5-sqrt(3-x)}}}


{{{x+10=(5-sqrt(3-x))^2}}}


{{{x+10=25-10*sqrt(3-x)+3-x}}}


{{{x+10=28-10*sqrt(3-x)-x}}}


{{{x+10-28+x=-10*sqrt(3-x)}}}


{{{2x-18=-10*sqrt(3-x)}}}


{{{(2x-18)^2=(-10*sqrt(3-x))^2}}}


{{{(2x-18)^2=100*(3-x)}}}


{{{4x^2-72x+324=100*(3-x)}}}


{{{4x^2-72x+324=300-100x}}}


{{{4x^2-72x+324-300+100x=0}}}


{{{4x^2+28x+24=0}}}


{{{4(x^2+7x+6)=0}}}


{{{4(x+6)(x+1)=0}}}


{{{x+6=0}}} or {{{x+1=0}}}


{{{x=-6}}} or {{{x=-1}}}


So the possible solutions are {{{x=-6}}} or {{{x=-1}}}


I'll let you check your answers


Note: a check is crucial when dealing with radical equations since one of those possible solutions may not even be a solution at all.