Question 35044
{{{ sqrt(x) = sqrt(x-2) - 4 }}}


Now square both sides:
{{{ (sqrt(x))^2 = (sqrt(x-2) - 4)^2 }}}
{{{ x = (sqrt(x-2) - 4)(sqrt(x-2) - 4) }}}
{{{ x = sqrt(x-2)sqrt(x-2) - 4sqrt(x-2) - 4sqrt(x-2) (-4)(-4)) }}}
{{{ x = (x-2) - 8sqrt(x-2) + 16 }}}
{{{ x = x - 8sqrt(x-2) + 14 }}}
{{{ 0 =  - 8sqrt(x-2) + 14 }}}
{{{ 8sqrt(x-2) = 14 }}}
{{{ sqrt(x-2) = 14/8 }}}
{{{ sqrt(x-2) = 7/4 }}}
{{{ x-2 = (7/4)^2 }}}
{{{ x-2 = 49/16 }}}
{{{ x = 2 + 49/16 }}}
{{{ x = 32/16 + 49/16 }}}
{{{ x = 81/16 }}}


Now, if you put this value into the original and take the square root, remember that that gives either 9/4 OR -9/4.


jon.