What number should be added to both sides of the equation to complete the square x^2+12x=11

36 should be added to both sides because 12/2= 6 then you square 6 to get 36 and that should be it.

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graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.