SOLUTION: Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) (3)(sqrt 4x &#8722; 7) + 2 = (sqrt 9 &#8722; x)= 17 <img src

Let one of the square roots equal to a letter

Let 

Then we have:



Isolate the remaining radical term on the left



Square both sides:











Now since  , 







Isolate the square root term:



Divide through by 4



Square both sides:













That may factor, but it would take longer to
factor it than to use the quadratic formula,
so I'll just use the quadratic formula:

 
 
 

 

  

Using the +

 

  

 

Using the -

 

  

 

So the solutions are  and 

But we must check to see if they are really solutions:

checking 












checking 














They both check.

Edwin