00:03
Once again, welcome to a new problem.
00:06
We're dealing with quadratics.
00:09
And when you think about quadratics, you're thinking about combination of linear functions.
00:19
Linear functions as a product.
00:24
So we're looking at linear functions as a product.
00:27
And in that sense, let's say we have x plus 2 and x plus 3.
00:32
What's going to happen? we're going to use the foil.
00:35
Method and foil means we're multiplying those two you get x squared that's the fast one and then also multiplying the outside of this is outside and that's going to give us plus 3x and then we multiply the inside that's going to give us plus 2x and then of course the last set of values, which is this constant.
01:04
So 3 times 2 is 6.
01:06
And so our quadratic becomes 5x plus 6.
01:12
If we wanted to, this is a function.
01:14
If we wanted to make the function an equation, we'll make it equal to 0.
01:19
And there are multiple ways of solving it.
01:22
We can solve it using the quadratic formula, which is x equals to minus b.
01:31
Plus minus radical b squared minus 4a c over 2a for example or we could take the same problem and factor it out as x plus 2 and x plus 3 equals to 0 and so that means the two solutions are negative 2 and negative 3 we could also take the same problem and complete this score so subtracting 6 on both sides.
02:07
So we have 5x equals to negative 6.
02:11
And then we obviously are going to take the coefficient of the middle term, which is 5 over 2 divided by 2 and square the result.
02:26
So we end up with x squared plus 5x plus 5 over 2 squared.
02:33
Squared and this is going to give us this is going to give us negative 6 plus 5 over 2 squared and we do know that we can make this the same as x plus 5 over 4 squared why because if you foil this when you get x squared plus twice 5 over 4 x plus plus 5 4 x plus 5 actually, this is 5 for 2, sorry.
03:12
This is 5 over 2, so completing the square.
03:17
And then this becomes 5 over 2 squared.
03:21
So we get x squared plus 5x plus 5 over 2 squared, which is exactly the same as what we have there.
03:31
And then we make it equals to negative 6 plus 2 and 5 over 4.
03:36
Get the lcd, so x plus 5 over 2 squared, becomes the same as negative 24 plus 25, all over 4, which is negative or positive 1 4th.
03:49
And so if i wanted to solve for x on both sides, i would get x plus 5 over 2 is the same as plus minus 1 half.
03:59
So x becomes the same as 5 or 2 plus minus 1 half.
04:04
That's completing the square.
04:06
So we have a problem.
04:09
The first problem we're given x squared plus 18x plus 32 equals to 0.
04:17
Solved by completing the square.
04:23
So what's going to happen is we will subtract 32 from both sides.
04:31
That's going to give us negative 32 on this side, and then we take the coefficient of 18 divided by 2, and then square the results.
04:41
We can put the square, so we have x squared plus 18x plus 18 over 2 squared equal to negative 32, plus 18 over 2 squared...