√(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: