Answer:
Step-by-step explanation:
Trying to factor as a Difference of Squares :
 1.1      Factoring:  r2-96 
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 : 96 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step  1  :
  r2 - 96  = 0 
Step  2  :
Solving a Single Variable Equation :
 2.1      Solve  :    r2-96 = 0 
 Add  96  to both sides of the equation : 
                      r2 = 96
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      r  =  ± √ 96  
 Can  √ 96 be simplified ?
Yes!   The prime factorization of  96   is
   2•2•2•2•2•3 
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).
√ 96   =  √ 2•2•2•2•2•3   =2•2•√ 6   =
                ±  4 • √ 6
The equation has two real solutions  
 These solutions are  r = 4 • ± √6 = ± 9.7980  
 
Two solutions were found :
                   r = 4 • ± √6 = ± 9.7980
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