SOLUTION: solve the following for x, square root 5x-15 all under one - square root x +1 all under one = 2

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Question 624279: solve the following for x,
square root 5x-15 all under one - square root x +1 all under DISABLED_event_one= 2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%285x-15%29-sqrt%28x%2B1%29=2 , adding sqrt%28x%2B1%29 to both sides, turns into
sqrt%285x-15%29=sqrt%28x%2B1%29%2B2
Squaring both sides, we get 5x-15=x%2B1%2B4%2Asqrt%28x%2B1%29%2B4
Adding -x-5 to both sides we get
4x-20=4%2Asqrt%28x%2B1%29
Dividing both sides by 4 we get
x-5=sqrt%28x%2B1%29
Suqaring both sides again, we get
x%5E2-10x%2B25=x%2B1
Adding -x-1 to both sides, we get
x%5E2-11x%2B24=0
Factoring, we get
%28x-3%29%28x-8%29=0
The solutions to x%5E2-11x%2B24=0 are x=3 and x=8.
Those could be solutions of the original equation, or could be extraneous solutions, introduced by all that squaring of both sides.
We must test them in the original equation.
x=3 gives sqrt%285x-15%29=0 while sqrt%28x%2B1%29=sqrt%284%29=2,
so sqrt%285x-15%29-sqrt%28x%2B1%29=-2
showing thatx=3 is not a solution of the original equation.
x=8 gives sqrt%285x-15%29=sqrt%2840-15%29=sqrt%2825%29=5 while sqrt%28x%2B1%29=sqrt%289%29=3,
so sqrt%285x-15%29-sqrt%28x%2B1%29=5-3=2
showing that highlight%28x=8%29 is the solution.