SOLUTION: Solve the following equation for ‘x’ and check for extraneous solutions: {{{sqrt(4-x) - sqrt(x+6) =2}}}

Isolate one of the radical terms:



Square both sides:



Take away the radical and square on the left.
Write expression squared on the right as multiplied by itself:



Use FOIL on the right:

    F  O    I    L 


Simplify:







Isolate the radical term:



Divide all three terms by -2



Square both sides:



Write expression squared on the left as multiplied by itself 
Take away the radical and square on the right. 
Don't forget to square the -2 on the right as +4



Use FOIL on the left, distribute on the right side:



Simplify



Get 0 on the right



Factor



Use zero-factor principle:

 gives 

 gives 

Test  in the original equation to see if it 
is a correct solution or an extraneous one:













That checks, so  is a correct solution.

Test  in the original equation to see if it 
is a correct solution or an extraneous one:













That does not check, so  is an extraneous solution and
must be discarded.

The only solution is 

Edwin