Question 163137
<pre>
Hi, this is the problem I was told to do:

[SQRT(2x + 2)] - [SQRT(x - 3)] = 2
or
&#8730;(2x+2) - &#8730;(x-3) = 2

I've been told to FOIL this problem, but I don't understand how to FOIL it if its subtracting and not
multiplying. What I do know is that the answer is equal to 7.
Thanks in advance.
*****************<font color = blue><font size = 2><font face = tahoma><b>
      {{{sqrt(2x + 2) - sqrt(x - 3) = 2}}}
This might be easier and less confusing if one of the radicals is moved to the right side. So, let's choose {{{- sqrt(x - 3)}}} to do that with. 
                    {{{sqrt(2x + 2) = 2 + sqrt(x - 3)}}} ----- Adding  {{{sqrt(x - 3)}}} to both sides
               {{{(sqrt(2x + 2))^2 = (2 + sqrt(x - 3))^2}}} -- Squaring both sides
               {{{(sqrt(2x + 2))^2 = (2 + sqrt(x - 3))(2 + sqrt(x - 3))}}} 
                        {{{2x + 2 = 4 + 2sqrt(x - 3) + 2sqrt(x - 3) + (sqrt(x - 3))^2}}} ---- FOILing right-side
                        {{{2x + 2 = 4 + 4sqrt(x - 3) + x - 3}}}
                        {{{2x + 2 = 1 + 4sqrt(x - 3) + x}}}
             {{{2x + 2 - 1 - x = 4sqrt(x - 3)}}}
                          {{{x + 1 = 4sqrt(x - 3)}}}
                      {{{(x + 1)^2 = (4sqrt(x - 3))^2}}} ---- Squaring both sides
                 {{{x^2 + 2x + 1 = 16(x - 3)}}}
                 {{{x^2 + 2x + 1 = 16x - 48}}}
{{{x^2 + 2x + 1 - 16x + 48 = 0}}}
            {{{x^2 - 14x + 49 = 0}}}
                     {{{(x - 7)^2 = 0}}}
                          x - 7 = 0___x = 7

             <font color = red><font size = 3>You can do the CHECK!!</font></font></font></font></font></b></pre>