Question

How do you solve `k^2+ 8k + 12 = 0` by completing the square?

Answer 1

`k=-6` or `k=-2`

Explanation:

To solve `k^2+8k+12=0`, by completing the square method

remember `(k+a)^2=k^2+2ka+a^2`

Now here we have `k^2+8k` in place of `k^2+2ka`, hence `2a=8` or `a=4` and we should have `a^2` or `4^2=16` in addition to `k^2+8k` to make it a square.

Hence we can write `k^2+8k+12=0` as

`k^2+8k+16-16+12=0`

or `(k+4)^2-4=0`

or `(k+4)^2-2^2=0`

As now this is in the form `a^2-b^2` which can be factorized as `(a+b)(a-b)`, we will have

`(k+4+2)(k+4-2)=0` i.e, `(k+6)(k+2)=0`

Hence either `k+6=0` or `k+2=0` or

`k=-6` or `k=-2`