Question 1016797: √(2x+5) + √(x+6) = 9
√(2x+5) = square root of (2x +5); √(x+6)= square root of (x+6)
Here is how far I got:
√(2x+5) + √(x+6) = 9
√(x+6)= 9-√(2x+5)
(√(x+6))squared= (9-√(2x+5))squared
x+6 = 81-18√((2x+5))+ 2x +5
x+6 = 86 - 18(√(2x+5))+2x
x -2x + 6 - 86 = -18(√(2x+5))
-x - 80 = -18(√(2x+5))
(-x - 80)/-18 = (-18(√(2x+5)))/-18
[(-x - 80)/-18]squared = [√(2x+5)] squared
(x squared + 160x + 6400)/324 = 2x +5
(x squared + 160x + 6400)/324 = (648x +1620)/324
(x squared -488x +4780)/324 = 0
[(x-10)(x-478)]/324 = 0
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621)   (Show Source):
You can put this solution on YOUR website! You messed-up about half-way down your steps. After squaring the first time, simplify, as you did, but then you need to isolate the radical still present and square both sides again.
Start from here:
Instead of trying to completely isolate the radical, just isolate the entire radical term, .... AND SQUARE BOTH SIDES THAT WAY.
 ----square both sides!
Simplify, and solve.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! √(2x+5) + √(x+6) = 9
√(2x+5) = square root of (2x +5); √(x+6)= square root of (x+6)
Here is how far I got:
√(2x+5) + √(x+6) = 9
√(x+6)= 9-√(2x+5)
(√(x+6))squared= (9-√(2x+5))squared
x+6 = 81-18√((2x+5))+ 2x +5
x+6 = 86 - 18(√(2x+5))+2x
x -2x + 6 - 86 = -18(√(2x+5))
-x - 80 = -18(√(2x+5))
(-x - 80)/-18 = (-18(√(2x+5)))/-18
[(-x - 80)/-18]squared = [√(2x+5)] squared
(x squared + 160x + 6400)/324 = 2x +5
(x squared + 160x + 6400)/324 = (648x +1620)/324
(x squared -488x +4780)/324 = 0
[(x-10)(x-478)]/324 = 0
You did a really great job up to this point: (x squared + 160x + 6400)/324 = (648x +1620)/324 --------> 
By now, you should notice that the DENOMINATORS are equal, so we just set the NUMERATORS equal to each other, as follows:
 , WITHOUT the denominator: 324, and NOT (x squared -488x +4780)/324 = 0.
After factoring, as you did,  [(x-10)(x-478)]/324 = 0, but  instead.
Thus, you end up with:  . However, x = 478 is an EXTRANEOUS solution, so the only solution is: 
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