Question 67703
 1) x^2 + 10x +25 , let k=25 then (x+5)^2
 2) x^2 – 4x + 4-4+2 = 0 (add and subtract 4)then (x-2)^2-2=0 then (x-2)^2=2
(x-2)=+sqrt(2) or (x-2)=-sqrt(2)
  x1=2+sqrt(2)  or x2=2-sqrt(2)
 3)x2 + 2x + 5 = 0? then x^2+2x+1+4= then (x+1)^2=-4 so no solutuin.
or check discriminant D= 2^2-4.5.1=-16
 4)x+7/x=8 then x^2-8x+7=0 then (x-7)(x-1)=0 then x1=7 or x2=1
 5)Solve the equation: x – 3 – sqrt x – 1 = 0? 
 x-3=sqrt(x-1) take square of both sides then x^2-6x+9=x-1 then  x^2-7x+10=0 then factorize (x-2)(x-5)=0 x1=5 or x2=2  check both solutions then only 5 satisfies the original equation.
 6)x + 2 – 2 sqrt x + 2 = 0? x+2=2 sqrt x + 2 then take square of both sides, x^2+4x+4=4(x+2) then x^2+4x+4=4x+8  then x^2=4 the x1=2 or x2=-2  check both solutions. If x1=2 then 4-2.2=0 satisfies x2=-2 also satisfies so solutions {2 ,-2}
 7)2 <| x – 10 | < 3   
then there are two conditions I) -3<x-10<3 then 7 <x<13 
the second condition 2< x-10 then x> 12 or 2 <-x+10 then   
   7<x<8  or  12<x<13