Question 87868
First add +3 to each side of the equation:

x^2-6x-3=0
x^2 -6x + ___ = 3+ ____ 


Take half of the x coefficient, -6, which is -3, and square which is 9.  Add +9 to each side:
{{{x^2 -6x+ 9= 3+9}}}
{{{(x-3)^2 = 12}}}


Square root both sides:
{{{x-3= 0+-sqrt(12)}}}


Add +3 to each side:
{{{x= 3+-sqrt(12) }}}


Simplify the square root:
{{{x= 3+-sqrt(4)*sqrt(3) }}}
{{{x= 3+2*sqrt(3) }}} or {{{x=3-2*sqrt(3) }}}


R^2  Retired from SCC