in this lesson we are going to look at how to do quadratic equations now first of all what is a quadratic equation let me first show you what is not a quadratic equation this over here is a normal equation that you would have seen in probably grade 6 7 8 9 where we just have X's now if I add an x to the power of 2 then all of a sudden it is called a quadratic equation and when we have a quadratic equation you have to solve it completely differently or in a complete different way to normal equations but be careful sometimes it looks like a quadratic equation but it actually is not let me show you an example what would happen here if we had to take for example this x squared over to the left hand side is that you would end up with something like 4 plus x squared minus x squared equals to 3x and these X squares would cancel out so what looked like a quadratic equation in the beginning actually turned out to be a normal equation so we will only say that it is a quadratic equation if there is an x squared that does not cancel out with another x squared here is another example of a quadratic equation I'm now going to show you how to solve a quadratic equation so what you do let's say we have an example like this all right so there we have a quadratic equation because it's got that x squared that we spoke about step one move everything to one side so for example this 9 we're going to move over to the left so it's going to become x squared minus 8x minus 9 equals to zero when you see the zero that's a good thing you want the zero on the left or the right it doesn't really matter but you do want that zero once you have the zero then you're gonna factorize now there are many different ways that you could be asked to factorize we know that there is difference of squares common factors trinomials so look out to see which type of factorizing you need to do if you're quite good with your factorizing you would know that this over here is a trinomial so we would have to factorize it as a trinomial so we'll have two brackets and it would be x minus nine and X plus one what you now do when you've got these brackets is you say x minus 9 must be equal to zero or X plus one must be equal to zero and then you go and you solve each of those so this one here would be that x equals to nine or and this one would say that X is equal to minus one now we are going to have a look at four examples for the first example we know that it's quadratic because it's got that x squared and it's not going to cancel out so remember step one get everything to one side so I'm going to say x squared minus 3x I'm going to bring the 4 over there we go now I've got the zero the zero is good what we now do is we factorize this is a trinomial so it's going to be x minus 4 and X plus 1. I then say x minus 4 is equal to 0 or X Plus 1 is equal to zero this then gives me X is equal to 4 or X is equal to negative one here's number two we already have the zero so that's step one complete now we factorize remember it's not always going to be a trinomial this is actually a difference of squares so we open up two brackets where it'll be x minus 2 and X plus two remember that's our difference of squares work and so we're going to end up with X is equal to 2 or X is equal to negative two actually I skipped a step there I do apologize I should say to be more or the more structured approach is to say x minus 2 is equal to zero or X plus 2 is equal to zero you then see that X is equal to 2 or X is equal to negative two in question three we've already got the zero so then we can factorize this over here is a trinomial so we open up our two brackets and we get x minus eight X plus one we then say x minus eight is equal to zero or X plus one is equal to zero this then means that X is equal to eight or X is equal to negative one and our last example this is definitely quadratic because it's got this x squared so what we do is we make the zero first so we take everything to the one side like that then we factorize but now some of you at home are saying Kevin what type of factorizing is this it's not a trinomial it can't be a difference of squares ah but guys this is actually a common factor you can take out an X so if you take out an X you would be left with x minus 3 in the bracket now what you do is pretend that this one is its own little bracket so then you can say X is equal to zero or x minus 3 is equal to zero and so this one already is simplified so we'll just say x is equal to zero or X is equal to