First recall that the quadratic formula used to solve for a quadratic equation of the form   ax² + bx + c = 0   is as follows:

          x = (-b ± √(b² - 4ac))/2a

For the equation  x² + 6x - 2 = 0 ,   a = 1 ,  b = 6 ,  c = -2 . We use these values for a, b, and c in the quadratic formula to solve for x:

     x = (-6 ± √(6² - 4·1·-2))/2·1

       = (-6 ± √(36 + 8))/2

       = (-6 ± √44)/2

Note:     √44 = √4·√11 = 2·√11

     x = (-6 ± √44)/2

       = (-6 ± 2√11)/2

Note:     -6 ± 2√11 = 2·(-3 ± √11)

     x = (-6 ± 2√11)/2

       = 2(-3 ± √11)/2

       = 2(-3 ± √11)/2

       = -3 ± √11

Thus,   x = -3 ± √11