00:01
Factor and complete the square on both sides of this equation.
00:03
So we're going to pull out a 9 and group our x terms.
00:06
We're going to have 9x squared plus 6x, and then we're going to have plus 9 times y squared minus 6 over 9, which is 2 thirds, y, and that's going to equal negative 64.
00:43
That was just a regrouping and reorganizing.
00:48
Okay, so completing the square, half of 6.
00:50
Is 3, so we're going to add 9.
00:53
Because of that coefficient of 9 out front, that really means we're going to be adding 81 to both sides.
01:01
Completing the square for the y, we're going to have half of two -thirds is one -third, and one -third squared is one -ninth.
01:11
Because of its coefficient, it's the same thing as adding one to both sides.
01:24
So writing this in a circle format, we're going to have x plus 3 squared, plus y minus one -third squared is going to equal 18 divided by 9, which is 2.
01:44
Negative 64 plus 81 plus 1 is 18.
01:48
And then we divide it by 9...
