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

1 Answer
Shwetank Mauria
May 27, 2016

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

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