00:02
We have a function g of x equals 2x squared plus 5x.
00:07
We need to find all of the values for x so that our function is equal to 12.
00:12
We'll start by using algebraic methods, and then we'll jump over to desmos to see what it looks like on a graph.
00:19
To find the values of x so that the function is equal to 12, we need to first substitute 12 for our function.
00:26
So 12 is equal to 2x squared plus 5x.
00:32
We know that in order to solve a polynomial equation, it needs to be set equal to 0.
00:38
So subtract 12 from both sides of the equation, and we have 0 equals 2x squared plus 5x minus 12.
00:48
Now we can factor to solve the equation.
00:52
Using the ac method, let's find ac.
00:55
2 times negative 12 is negative 24.
01:00
We need the factor pair of negative 24 that when added, gives us the value of our middle term, which is five.
01:09
Since we have a negative product and a positive sum, we know one factor has to be positive while the other is negative.
01:16
We also know the positive factor has to be the greatest factor because our middle term is positive.
01:22
So the factor pair of negative 24 that will add to give us positive 5 is positive 8 and negative 3.
01:31
Let's rewrite our trinomial with our new middle terms.
01:36
So we have 2x squared plus 8x minus 3x minus 12.
01:46
This is still equal to 0.
01:50
Next we can group the first two terms and the last two terms and factor out the greatest common factor for each grouping.
01:59
2x squared plus 8x, the greatest common factor is 2x...