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:
$2X^2 +4X$

$2(X^2 + 2X)$

$2(X + 1)^2$

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