#color(red)(Commenci ng)# #color(red)(compl e ti ng)# #color(red)(the)# #color(red)(squ are)# #color(red)(method)# #color(red)(now,)#

1) Know the formula for the perfect quadratic square, which is,

#(ax+-b)^2 = ax^2+-2abx+b^2#

2) Figure out your #a and b# values,

#a=# coefficient of #x^2#, which is #1#.

#color(red)(b=6/(2(1)) = 3)#

3) Move the #4# over to the right hand side,

#x^2+6x=-4#

4) Add #color(red)(b^2)# on both sides of the equation, giving you an overall net of 0, hence not affecting the result of the equation,

#x^2+6x+color(red)(3^2)=-4+color(red)(3^2)#

#(x+3)^2=5#

5) Square root both sides,

#x+3=+-sqrt(5)#

6) Move the #3# over to the right side,

#x=+-sqrt5-3#

7) Calculate the two values of #x#,

#x=-0.76393202 or x=-5.23606797#