How do you complete the square for $x^2 + 11x$ ?

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Answer 1 · 2015-07-19T09:32:29

$x^2+11x = (x+11/2)^2-11^2/(2^2) = (x+11/2)^2-121/4$

In general,

$ax^2+bx+c = a(x+b/(2a))^2+(c-b^2/(4a))$

Notice the $b/(2a)$ term.

In our case $a=1$ and $b=11$ hence the $11/2$

How do you complete the square for x^2 + 11xx^2 + 11x?