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

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

RELATED QUESTIONS
Help! I am stuck on solving a radical equation. The original problem is this:... (answered by tutorcecilia)
i have this formula: y=1000e^-0.056x this si the line of best fit. i need to find x when (answered by ewatrrr)
I am very sorry this is not from a text book. I am working on compound inequalities:... (answered by stanbon)
X ^ 4 � 2 x ^ 2 = 8 That is: x to the fourth minus two x squared equals eight. Find (answered by Earlsdon)
please help me with this problem. i am having trouble because i am getting stuck on it.... (answered by checkley77)
Hello, I am having issues with this problem...I understand that I have to square both... (answered by jim_thompson5910)
So this is literal equations, i didnt know what catagory to put this question under so I... (answered by josgarithmetic,MathTherapy)
I have to complete the square for this problem.. x^2+13=(-14x)I have this I added 14... (answered by tutor_paul)
Hi, I am kind of stuck on this question. I keep getting 1/7 but that doesn't make sense... (answered by Alan3354)