00:02
So i'm given a quadratic equation that is a model for a certain business production.
00:10
And i'm asked to figure out what the number of items are if i have a cost factor of 9 ,500.
00:19
So all i need to do here is substitute my value and then factor my quadratic.
00:25
So the cost for c is 9500.
00:28
And then i already have the equation of x squared minus 15x plus 50.
00:35
And so i'm going to subtract 9500 from each side so that i have my quadratic form, or standard form of a x squared plus bx plus c, which is actually going to be minus c.
00:51
So it's going to be 9450.
00:57
And i am going to have to factor this, which, 9450 seems like a really big number but i'll start with some good easy big numbers so first i'll do 50 so 94 50 divided by 50 is 189 okay so 50 and 189 so we have 94 50 all right so i'm looking for two factors that when i multiply them obviously i get my 9450, but when i add them or subtract them, i'm going to get 15 because when i factor this, my a coefficient is 1.
01:41
So i know i'm just going to have x here and x here.
01:44
But this is a negative c term.
01:46
That means one of my factors is going to be addition and the other one's going to be subtraction.
01:51
So if i do 189 minus 50, i get a lot more than 15.
01:55
So i'm going to need to break this down a little bit more.
01:57
So i'm going to break this down by, we'll do nine.
02:01
So nine times 21.
02:04
So if i do, let's see, no, that's still not going to work.
02:10
50 is too big because 50 times 9 is like 450.
02:13
So that's not going to work.
02:14
So i need to break this down.
02:16
We'll do 10 times 5.
02:18
All right...