00:01
The first thing i like to do with these types of problems is just put the x with the x squared term, and then a little blank in here, and then y squared with its term of negative 8 y, and then a blank, and while i'm at it, go ahead and move that 32 to the right side, which would be subtracting over.
00:24
That's why it's negative 32.
00:26
So the process on completing the square is the same for both of these.
00:30
You take that number negative 10 divided by 2 and then you square that and you get 25.
00:37
That's only acceptable if you also add 25 to the other side because of the equation, the equality.
00:44
Do the same thing with 8.
00:46
Negative 8 divided by 2 is negative 4.
00:50
And the moment you square that, you get 16.
00:53
So you can only do that if you add 16 to the right side as well.
00:58
So now what you have is a perfect square trinomial, and the factors of 25 that had to be negative 10 are negative 5 and negative 5.
01:08
But instead of writing it twice, we can write it 1 squared.
01:11
If you don't believe me, foil it back out and you'll get back up here.
01:15
Same thing with this y.
01:18
Hopefully you notice the trick.
01:20
It's always that number.
01:21
That's why this works.
01:22
And then on the right side, you have negative 32 plus 25 plus 16...