SOLUTION: Solve: √x-6 + √x = 6 (x-6 is all under the square root)

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Question 640044: Solve: √x-6 + √x = 6 (x-6 is all under the square root)
Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Öx - 6 + Öx = 6

Isolate the more complicated radical term:

     Öx - 6 = 6 - Öx

Square both sides:

  (Öx - 6)² = (6 - Öx)²
     
      x - 6 = (6 - Öx)(6 - Öx)
      
      x - 6 = 36 - 6Öx - 6Öx + x

      x - 6 = 36 - 12Öx + x

Isolate the radical term on the right

              42 = 12Öx

Divide both sides by 6

               7 = 2Öx

Square both sides:

              7² = (2Öx)²

              49 = 4x

               = x

You must check all radical equation because sometimes
squaring both sides often introduces extraneous "solutions".  
It'll be easier to check if we convert  to a decimal 12.25

               Öx - 6 + Öx = 6

       Ö12.25 - 6 + Ö12.25 = 6

          Ö6.25 + Ö12.25 = 6

               2.5 + 3.5 = 6

                       6 = 6                                

So the solution is  or 12.25

Edwin
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


In the future, use sqrt(*expression*) to indicate square root. Use either sqrt[n](x) or root(x,n) to indicate

The first thing is that you don't want to have two terms with a radical on one side of an equation if you can help it. In this case, add to both sides of the equation:



Square both sides



Rearrange, collect terms, etc.



Multiply both sides by and then reduce the fraction in the RHS.



Square both sides:



John

My calculator said it, I believe it, that settles it
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