Question 58843
{{{ sqrt(x+6)+sqrt(2-x)=4 }}}
{{{(sqrt(x+6)+sqrt(2-x))^2=4^2}}}
{{{(sqrt(x+6)+sqrt(2-x))(sqrt(x+6)+sqrt(2-x))=16}}}
{{{(x+6)+sqrt(x+6)sqrt(2-x)+sqrt(x+6)sqrt(2-x)+(2-x)=16}}}
{{{8+2sqrt(x+6)sqrt(2-x)=16}}}
{{{-8=2sqrt(x+6)sqrt(2-x)}}}
{{{-4=sqrt(x+6)sqrt(2-x)}}}
{{{(-4)^2=(sqrt(x+6)sqrt(2-x))^2}}}
{{{16=(x+6)(2-x)}}}
{{{16=2x-x^2+12-6x}}}
{{{0=-x^2-4x-4}}}
*[invoke quadratic "x", -1, -4, -4 ]


Let's check if the solution -2 works:

{{{sqrt(-2+6)+sqrt(2-(-2)) = sqrt(4) + sqrt(4) = 2+2 = 4}}}

There you go!