Question 128955
I think you mean {{{x^2+11x-6=0}}}


Step 1:  Add the additive inverse of the constant term to both sides.  For this problem, add 6 to both sides:


{{{x^2+11x=6}}}


Step 2:  Divide through by the coefficient on the {{{x^2}}} term.  For this problem, that is 1, so you don't have to do anything.


Step 3:  Divide the coefficient on the {{{x}}} term by 2.  For this problem, that becomes {{{11/2}}}.


Step 4:  Square the result of step 3.  For this problem:  {{{121/4}}}


Step 5:  Add the result of step 4 to both sides of the equation.  For this problem:


{{{x^2+11x+(121/4)=6+(121/4)}}}


{{{x^2+11x+(121/4)=(24+121)/4}}}


{{{x^2+11x+(121/4)=145/4}}}


Step 6:  Factor the left:


{{{(x+(11/2))^2=145/4}}}


Step 7: Take the square root of both sides:


{{{x+(11/2)=sqrt(145/4)}}} or {{{x+11/2=-sqrt(145/4)}}}


{{{x=(-11+sqrt(145))/2}}} or {{{x=(-11-sqrt(145))/2}}}


Yes, these numbers are a horror, but certainly prettier than what you generally encounter in real life situations.  By the way, {{{sqrt(145)}}} is reduced to simplest terms because there are no perfect square factors of 145 -- the prime factorization is 5 * 29.