Question

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

Answer 1

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`