Answer: x = 2 • ± √2 = ± 2.8284
Step-by-step explanation:
Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)
Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 =  
         A2 - B2
Note :  AB = BA is the commutative property of multiplication.  
Note :  - AB + AB equals zero and is therefore eliminated from the expression.
Check : 8 is not a square !!  
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step  1  :
  x2 - 8  = 0  
Step  2  :
Solving a Single Variable Equation :
 2.1      Solve  :    x2-8 = 0  
 Add  8  to both sides of the equation :  
                      x2 = 8  
  
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ 8  
 Can  √ 8 be simplified ?
Yes!   The prime factorization of  8   is
   2•2•2  
To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).
√ 8   =  √ 2•2•2   =
                ±  2 • √ 2  
The equation has two real solutions  
 These solutions are  x = 2 • ± √2 = ± 2.8284  
  
Two solutions were found :
                   x = 2 • ± √2 = ± 2.8284
Not sure what you need help with, but I hope I helped you somehow.