Question 870637
{{{sqrt(3x+3)+sqrt(x+2) = 5}}}



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



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



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



{{{3x+3 = 25-10*sqrt(x+2)+x+2}}}



{{{3x+3 = 27-10*sqrt(x+2)+x}}}



{{{3x+3-27-x=-10*sqrt(x+2)}}}



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



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



{{{4x^2-96x+576=100(x+2)}}}



{{{4x^2-96x+576=100x+200}}}



{{{4x^2-96x+576-100x-200=0}}}



{{{4x^2-196x+376=0}}}



{{{4(x^2-49x+94)=0}}}



{{{x^2-49x+94=0/4}}}



{{{x^2-49x+94=0}}}



{{{(x-47)(x-2)=0}}}



{{{x-47=0}}} or {{{x-2=0}}}



{{{x=47}}} or {{{x=2}}}



The *possible* answers are {{{x=47}}} or {{{x=2}}}



We need to check them.



-----------------------------------------------------------



Checking {{{x=47}}}



{{{sqrt(3x+3)+sqrt(x+2) = 5}}}



{{{sqrt(3*47+3)+sqrt(47+2) = 5}}}



{{{sqrt(141+3)+sqrt(47+2) = 5}}}



{{{sqrt(144)+sqrt(49) = 5}}}



{{{12+7 = 5}}}



{{{19 = 5}}} This is FALSE. So {{{x=47}}} is NOT a solution.



Checking {{{x=2}}}



{{{sqrt(3x+3)+sqrt(x+2) = 5}}}



{{{sqrt(3*2+3)+sqrt(2+2) = 5}}}



{{{sqrt(6+3)+sqrt(2+2) = 5}}}



{{{sqrt(9)+sqrt(4) = 5}}}



{{{3+2 = 5}}}



{{{5 = 5}}} This is TRUE. So {{{x=2}}} is a solution.



=============================================================


Final Answer: {{{x=2}}}