SOLUTION: Could you help me with this? {{{8sqrt(x-1)+1}}} = {{{x}}} Thank-you

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Question 93556: Could you help me with this?
=
Thank-you

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Could you help me with this?

 = 

Thank-you

 = 

Add -1 to both sides to get the radical 
term alone on the left:

   = 

Square both sides of the equation:

  = 

 = 

 = 

 = 

Switch left and right sides for convenience:

 = 

Get 0 on the right 

 = 

Factor left side by thinking of two whole numbers
which have product 65 and sum 66, whch are 65 and 1:

 = 0

Set each factor = 0

 gives 

 gives 

However we must check these answers because radical
equations often have extraneous answers, which are
not solutions.  

Checking 

 = 

 = 

 = 

 = 

 = 

 = 

So we know  is a valid solution.

Checking 

 = 

 = 

 = 

 = 

 = 

 = 

So as it turns out, both  and 
are valid solutions.

But be aware that this is not always the case.
Sometimes when you get two answers, one of them
will be a solution and the other will not check,
and thus must be discarded; sometimes neither one 
is a solution and the equation has no solution.
Just be sure to ALWAYS CHECK a RADICAL EQUATION.

Edwin



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