SOLUTION: please help! I'm getting stuck in the middle of this problem. I know to separate the radicals square both sides, then isolate radical but I am not coming up with the correct answ

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Question 30525: please help! I'm getting stuck in the middle of this problem. I know to separate the radicals square both sides, then isolate radical but I am not coming up with the correct answer. Any help is appreciated!
Thanks
Jane P.
sqrt(2x+5) + sqrt(x+6) = 9
Found 2 solutions by sdmmadam@yahoo.com, venugopalramana:
Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website!
sqrt(2x+5) + sqrt(x+6) = 9----(1)
sqrt(2x+5) = 9 - sqrt(x+6)
Squaring both the sides
[sqrt(2x+5)]^2 = [9 - sqrt(x+6)]^2
(2x+5) = 9^2+(x+6)-2X9X sqrt(x+6)
[using [sqrt(p)]^2 = p on the LHS (as well as later in the RHS
and formula: (a-b)^2 = a^2+b^2-2ab where here a=9,b = sqrt(x+6)]
2x+5 = 81+x+6-18sqrt(x+6)
(2x-x)+(5-81-6) = -18sqrt(x+6)
(x-82) = -18sqrt(x+6)
Squaring both the sides
(x-82)^2 = [-18sqrt(x+6)]^2
x^2-164x+6724 = 324(x+6)
x^2-164x+6724 = 324x +1944
x^2-164x-324x+6724-1944 =0
x^2-488x+4780 =0
(sum is -488 and productis +4780 and therefore the quantiies are(-478)and (-10))
x^2-10x-478x-4780 = 0
x(x-10)-478(x-10) = 0
xp-478p = 0 where p = (x-10)
p(x-478) = 0
(x-10)(x-478) =0 (putting p back)
(x-10) = 0 gives x = 10
(x-478) = 0 gives x = 478
Answer: x = 10 and x = 478
Verification: x = 10 in (1)
LHS=sqrt(2x+5) + sqrt(x+6)
=sqrt[(2X10+5)] + sqrt[(10+6)]
= sqrt[(25)] + sqrt[(16)]
=5+4
=9
=RHS
Regarding the other huge number looking at the small number 9 on the RHS tells us that at least one of the roots we should take negative to comply with the answer:
x = 10 in (1)
LHS=sqrt(2x+5) + sqrt(x+6)
=sqrt[(2X478+5)] + sqrt[(478+6)]
= sqrt[(961)] + sqrt[(484)]
= 31-22
=9
=RHS

Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
sqrt(2x+5) + sqrt(x+6) = 9
sqrt(2x+5)= 9 - sqrt(x+6) ...square both sides
2X+5=81+X+6-18*SQRT.(X+6)
X-82 = -18*SQRT.(X+6)...SQUARING AGAIN
X^2+6724-164X =324(X+6)=324X+1944
X^2- 488X+4780 = 0
X^2-10X - 478X+4780=0
X(X-10)- 478(X - 10)=0
(X-10)(X-478)=0...HENCE X-10 = 0 ....OR....X=10 WHICH IS CORRECT SINCE
sqrt(2x+5) + sqrt(x+6) =sqrt(2*10+5) + sqrt(10+6) = 5 + 4 = 9
X-478 = 0 OR ..X=478 IS AN EXTRANEOUS ANSWER OBTAINED DUE TO REPEATED SQUARING ...WE SHOULD IGNORE THAT