Squaring both sides gives:

`sqrt(x+10)=x-2`

Squaring both sides again gives:

`x+10=x^2-4x+4`

`x^2-5x-6=0`

`(x+1)(x-6)=0`

This gives us `x = -1` or `x = 6`.

CHECK:

Substituting `x = -1` in our original equation gives:

`"LHS"=root(4)(-1+10)=root(4)(9)`

`"RHS"=sqrt(-1-2)=sqrt(-3)`

Does not check OK

Substituting `x = 6` in our original equation gives:

`"LHS"=root(4)(6+10)=root(4)(16)=2`

`"RHS"=sqrt(6-2)=sqrt(4)=2`

Checks OK

So we conclude the solution is `x = 6`.