00:01
So we have a market equilibrium question that has to do with the demand of watches.
00:06
So the demand of watches is given by the first function p equals 7 ,000 minus 2x, where p represents the price of each of the watches and the x represents the quantity or number of watches demanded.
00:22
And then similarly, we have the supply equation p equals 0 .01x squared plus 2x plus 1 ,000, and the variables represent the same thing.
00:30
We want to know the market equilibrium, so where does the supply meet the demand? so at what quantity and at what price is what we're being asked.
00:37
So because both functions are equal to p, we're going to set them equal to each other.
00:41
So our demand function is going to be equal to our supply function.
00:48
And we are going to try to set this equal to zero so that we could then use the quadratic formula.
00:53
So i'm going to subtract 7 ,000 and i'm going to add 2x on both sides.
01:02
And so if i do that, i'm now going to have a function that says 0 equals 0 .01x squared plus 4x minus 6 ,000.
01:12
So i now have a nice quadratic in standard form that i can use the quadratic formula.
01:19
So negative b is negative 4 plus or minus the square root.
01:22
B squared is 16, 4 squared is 16.
01:25
So b squared minus 4 times a, 0 .01 ,000, times c, which is negative 6 ,000.
01:31
All over 2 times a, which is 0 .01.
01:36
So we're going to go ahead and simplify this...