How do I complete the square if the coefficient of #x^2# is not 1?

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Answer 1 · 2014-10-07T17:41:41

Remember that

#(ax + b)^2 = a^2x^2 + 2abx + b^2#

So the general idea to get #b^2# is by getting #x#'s coefficient,
dividing by #2a#, and squaring the result.

Example

#3x^2 + 12x#

#a = 3#
#2ab = 12#
#6b = 12#
#b = 2#
#3x^2 + 12x + 4 = (3x + 2)^2#

You can also factor out #x^2#'s coefficient.. and proceed with completing the square.

Example:
#2X^2 +4X#

#2(X^2 + 2X)#

#2(X + 1)^2#