so with the first one the way that you would solve this is you always have two options you could well not always but in one like this you could factorize that's where you make the brackets and if you don't feel like factorizing you could use the quadratic formula the one that looks like this and so very often when i don't feel like doing any factorizing i simply use the formula even though it might be something that's quite easy to factorize the formula works for any kind of trinomial or any kind of expression where the highest exponent is a two and so let's start with number one so with number one number one is typically something that is very easy to factorize and so i'm sure from your grade 10 and grade 9 knowledge factorizing is not a problem but this is the one where you would make the two brackets and you would end up with x minus four x plus one equals to zero and then your two answers would be when x minus four is equal to zero and x plus one is equal to zero therefore for the first one x would equal to four or x is equal to minus one and then of course you could use the formula and i'll show you how the formula works just for this first one so you fall in the formula exactly as you see it so it starts off with a minus then you put a bracket and full in the value of b now b is always this number that is in front of the x and so in that case it's a minus 3. you don't want to get into the habit of looking at that negative in front of the b and then instantly switching the negative and the negative into a positive rather stick to the basics and you'll see your amount of errors will be a lot less then over here we have the choice of plus and minus so you have to do both of them so i'm just going to start off with the plus square root then here's where i've seen many people who have been stuck in a test for up to 20 minutes trying to solve their formula which keeps giving them an error only to realize afterwards that it was because they didn't use a bracket for the b squared part and because they had a negative b value they kept getting an error inside the square root and so it is such a good habit if you can it's really going to help be helpful if you can just remember to use a bracket for that term specifically and so the b value is minus 3 because if you had to use just a minus 3 squared here that would be -9 but by putting it in a bracket it takes the negative into account and it just becomes a positive nine and then we're going to have minus and then the value of a i'm going to put that in a bracket the value of a is the one that's in front of x squared which in this case is just going to be the number one and then the value c is the number that has no x with it so that's just minus four also in a bracket notice how we just use brackets it just it's a lot safer that way then we're at the bottom we have two once again we open up a bracket and we put in the value of a you can then go type all of this on the calculator just as you see it putting brackets just as you've written them down and you would get an answer of you'd get an answer of 4 for the first one and then for the next step you would just switch this positive sign over here to a negative and that would give you the x equals to minus one so please don't get fall into the trap of believing that you can only use the formula for for instances when you can't find the the brackets that's not true you can use the formula whenever you like actually teachers often won't mention that but there's no harm in using the formula moving on to number two so remember when you're trying to solve an equation that only has x in it so for example something like this notice there's no x squared in these kinds of equations you take all the x's to the one side and all the numbers to the other side but as soon as we spot an x squared such as with number one and also with number two what you instantly want to do is take everything to the one side and make the other side equal to zero we can't keep the x's on one side and the numbers on the other side i've seen many students forget about that and then they try solve it like that and they get completely stuck so straight away as soon as there's an x squared everything to the one side it doesn't matter if you want to go left or right and then make the other side equal to zero and so for number two i'm just gonna write it over here i'm gonna bring this negative 10 over so it will become plus 10 and then the other side has nothing left over so that's 0. now this is what you want because this formula this quadratic formula only works when you've got a zero on the one side and if you would like to factorize you also need to have a zero on the other side and so this is one that can be factorized or you can use the formula once again but i'm just going to factorize this one and so you're going to end up with x minus 5 equals to 0 x minus 2 equals to 0 so therefore x is equal to 5 or x is equal to 2 and those are the two answers for that one number 3 which i'll just write up at the top so it's two x squared minus seven x plus three equals to zero straight away i wouldn't even try factorize that this one is one that can be factorized i only know that because i've looked at the questions before the video of course but in a test i wouldn't even waste time trying to factorize i would just plug that straight into the formula and so if you had to plug that into the formula it would look something like x is equal to then you say minus this is very important that minus i got from here that's part of the formula then i put a bracket and i put the b value itself which is also a negative okay then i'll choose a plus for now open the square root open up a bracket and plug the minus 7 in there minus 4 open a bracket 2 open another bracket the c value is 3 over 2 open a bracket and the a value is 2. you can then go plug all of that into the calculator as you see it you don't have to go individually go and simplify each part you can just plug that straight into the calculator and so this one gives you x equals to 3 and for the other one you're going to end up with x is equal to 0.5 or you could even write that as a half if you would like and so because we're getting nice answers like this that's also a clue that that original expression could in fact be factorized for those of you who are watching this and who did use the factorizing option then your brackets that you would have got would have been two x minus one and x minus three and so that would have given you the half and the three as your final answer number four negative x squared plus 11x minus 8. that would just be a formula one so i'm not going to show you all the processes but make sure when you're plugging that into the formula that you are plugging it in correctly by using brackets and for that one your answers are going to be 0.78 and 10 comma 2 2 rounded off to two decimal places number five is a really good one because i've noticed that people often panic when they get one like this it's a lot easier than all the others but it's that it's not the most common kind of question so when we had a question such as number one which was x squared minus three x minus four what did we do at this next step if we didn't use the formula then we did we made the two brackets but what is that process called it's factorizing right now factorizing isn't always going to be a trinomial factorizing could be difference of squares common factor and so we have to keep those in mind it's just that we often get the trinomial and so we believe that we always have to use a trinomial but for something like this you're not going to use a trinomial that's just a common factor and so the common factor there would be x you take that out and then you're left with x minus 3 equals to zero and then at this point people really do struggle as what to do at that x but remember you can think of that as its own little bracket and so you could simply say that x is equal to zero or x minus three is equal to zero therefore x is three and therefore x is obviously just zero and those are the two answers furthermore you could even use the quadratic formula which value would equal zero would it be the a b or c it would be the c right because usually the c comes after this three x over here and so that's also an option you could plug it into the formula number six is a brilliant question it's another area where i've seen people make mistakes i know it's very tempting to sometimes cancel out one of these x's and cancel out one of those x's and get x equals to four it's a very common mistake but remember that goes against of our rule that says as soon as you see an x squared you should take everything to the one side and make the other side equal to zero and so you're going to end up with x squared minus four x like that equal to zero and now we factorize like we did in number five where you take out a common factor of x you'd be left with x and x minus four and so you would get x is equal to zero because you can think of this as its own bracket or x minus four equals to zero so therefore for that one x would equal to 4 right because if you take the 4 over and x would equal to 0. so this technique over here does give you one of the answers but you lose out on the other answers and if you want to upset your teacher then you should just you should cancel this x like what i showed you here and you have red marks going all across your page and the last question for this video number seven don't even bother trying to factorize that in the test it's gonna waste a lot of time simply plug it into the formula and the answers that you should get for that one would be 2.3 usually it's two decimal places but if you see on your calculator when you do that one you're going to get 2.297 and so that does round to 2.3 and then the other answer is going to be 0.56 and that's the end of this video thank you for watching