For this case we must solve the following equation by completing squares:[tex]x ^ 2 + 6x-6 = 0[/tex]We add 6 to both sides of the equation:[tex]x ^ 2 + 6x = 6[/tex]We divide the middle term by 2, and square it:[tex](\frac {6} {2}) ^ 2[/tex]And we add it to both sides of the equation:[tex]x ^ 2 + 6x + (\frac {6} {2}) ^ 2 = 6 + (\frac {6} {2}) ^ 2\\x ^ 2 + 6x + (3) ^ 2 = 6 + 9[/tex]We rewrite the left part of the equation:[tex](x + 3) ^ 2 = 15[/tex]We apply root to both sides:[tex]x + 3 = \pm \sqrt {15}[/tex]We have two solutions:[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]Answer:[tex]x_ {1} = \sqrt {15} -3\\x_ {2} = - \sqrt {15} -3[/tex]