Solve by completing the square x^2+6x+3=0

X²+6x+ ___= -3+ ___

The blank is equal to (b/2)², which is, in this case, 9. However, I would leave it as (3)² on the left in order to re-write it.

X²+6x+(3)²=6
(X+3)²=6

See how the 3 dropped down?

X-3=±√(6)
X=3±√(6)

Note: Whenever you take the square root of something, you must include a ± because, for example, 2²=(-2)² and you must account for all possible answers.