Question 849769
Description: (rad of 4-x  PLUS the rad of x+6) all equal to 4 
can best be understood to mean:  {{{sqrt(4-x)+sqrt(x+6)=4}}}.


When you think you have finished finding the values for x, and you want to know if any is extraneous, you can check how the value works in the ORIGINAL equation.


CHECK -5.
{{{sqrt(4-(-5))+sqrt(-5+6)=4}}}?
{{{sqrt(9)+sqrt(1)=4}}}
{{{3+1=4}}}
TRUE!  
{{{x=-5}}}.


CHECK 3.
{{{sqrt(4-3)+sqrt(3+6)=4}}}?
{{{sqrt(1)+sqrt(9)=4}}}
{{{1+3=4}}}
TRUE.
{{{x=3}}}.


BOTH solutions work in the original equation.