x =(6-√108)/2=3-3√ 3 = -2.196
 x =(6+√108)/2=3+3√ 3 = 8.196
Step-by-step explanation:
Step  1  :
Equation at the end of step  1  :
2 • (x - 3)2 - 54 = 0
Step  2  :
 2.1   Evaluate :  (x-3)2  =  x2-6x+9Â
Step  3  :
Pulling out like terms :
 3.1    Pull out like factors :
   2x2 - 12x - 36  =   2 • (x2 - 6x - 18)Â
Adding  9 has completed the left hand side into a perfect square :
   x2-6x+9  =
   (x-3) • (x-3)  =
  (x-3)2  (x-3)1 =
   x-3
Now, applying the Square Root Principle to Eq. #4.3.1  we get:
   x-3 = √ 27
Add  3  to both sides to obtain:
   x = 3 + √ 27
Since a square root has two values, one positive and the other negative
   x2 - 6x - 18 = 0
   has two solutions:
  x = 3 + √ 27
   or
  x = 3 - √ 27
Solve Quadratic Equation using the Quadratic Formula
 4.4     Solving    x2-6x-18 = 0 by the Quadratic Formula .
 According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :
                                    Â
            - B  ±  √ B2-4AC
  x =  ————————
                      2A
  In our case,  A   =    1
                      B   =   -6
                      C   =  -18
Accordingly,  B2  -  4AC   =
                     36 - (-72) =
                     108
Applying the quadratic formula :
               6 ± √ 108
   x  =    —————
                    2
Can  √ 108 be simplified ?
Yes!   The prime factorization of  108   is
   2•2•3•3•3Â
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).
√ 108   =  √ 2•2•3•3•3   =2•3•√ 3   =
                ±  6 • √ 3
 √ 3  , rounded to 4 decimal digits, is   1.7321
 So now we are looking at:
           x  =  ( 6 ± 6 • 1.732 ) / 2
Two real solutions:
 x =(6+√108)/2=3+3√ 3 = 8.196
or:
 x =(6-√108)/2=3-3√ 3 = -2.196