in this video we're going to learn how to use the quadratic formula to solve a quadratic equation so here we have a quadratic equation that we're asked to solve and it says to give your answers to two decimal places when a question is written in this way it strongly suggests that we'll need to use the quadratic formula the quadratic formula is given by x equals negative b plus or minus the square root of b squared minus 4ac all divided by 2a now this is a formula that you'll need to memorize for your exams it won't be given to you but what do a b and c actually mean well when we write a quadratic equation out we tend to write it in this form ax squared plus bx plus c equals zero what that means is the number in front of the x squared would be a so in this one a would be two the number in front of the x would be b so in this case b would be five and the final term at the end the constant would be c so in this case c would be 1. let's have a look at how we can solve this question then we're going to write the quadratic formula on the left side of the screen along with the steps that we're going to go through the first step is to write it in the form ax squared plus bx plus c equals zero fortunately our quadratic is already in this form all this means is all of the terms need to be on the left and the right just needs to be zero the next step is to find the values of a b and c so a was the coefficient of x squared so that's two b was the coefficient of x so that's five and c was the constant term at the end so that's one step three is to substitute these into the formula so we're going to write out the formula again but everywhere there's an a we'll write 2 everywhere there's a b will write 5 and everywhere there's a c we'll write 1. so x equals negative b which is negative 5 plus or minus the square root of b squared which is five squared minus four times a which is times two and times c which is times one and all of this divided by two a and since a is two it's 2 times 2. the next step is to simplify we're going to tidy up a little bit we're going to keep x equals negative 5 plus or minus the square root but we're going to simplify what's inside the square root so if you do 5 squared you get 25 and then negative 4 times 2 times 1 is negative 8 and 25 take 8 is 17. you'll often have this question on a calculator paper though so you could probably just type that into your calculator and on the bottom we have 2 times 2 which is 4. the final step of the question is to write your solutions now there are two solutions at this point we have x equals negative 5 plus root 17 over 4 and x equals negative 5 subtract root 17 over 4. notice the difference between these is the positive here and the negative here i would then just type both of these into my calculator to get an answer remember the question said round to two decimal places so if you type the first one in you'll get x equals negative 0.22 and the second one would give you x equals negative 2.28 this next question is a little more difficult the first step is to write it in the form ax squared plus bx plus c equals zero last time it was already in this form but this time it's not you can tell because the right hand side is not equal to zero instead we have ten minus two x squared to get this to zero we're going to add two x squared and we're going to take away ten to remove those terms that would mean the right hand side is equal to zero and we should do the same to the left hand side so add 2x squared and take away 10. on the left side we've already got 1x squared and we're adding 2x squared so there's now 3x squared the minus 5x can stay as it is because we're not adding or taking away any x's and then we've got 7 and we're going to take away 10 7 take away 10 is negative 3. so now this is in the correct form ax squared plus bx plus c equals 0. step 2 find the values of a b and c we can see a is three b this time is negative negative five and c is also negative negative three step three substitute into the formula so we're going to write the formula out again but instead of a we'll write 3 instead of b negative 5 instead of c negative 3. the formula begins with x equals negative b but b is already a negative it's negative 5. so if we want negative b this actually switches back to a positive so x equals 5 plus or minus the square root of b squared now anytime you write a negative number i'd suggest you write it in brackets so instead of just 5 squared negative 5 in a bracket squared minus 4 times a and a is 3 and then times c which is negative 3 and again you can see i've used the bracket for that negative number all divided by 2a and a is three so it's two times three we'll then go to step four which is to simplify so x equals we'll keep the five and the plus or minus and then we have the square root again at this point you might just want to type what's inside the square root into your calculator so negative five in a bracket squared minus four times three times negative three and that will give you sixty-one all over two times three and two times three is six we can now separate this into our two solutions so we have first of all x equals 5 plus square root 61 over 6 and then we have x equals 5 minus square root 61 over 6. the difference here is the first one has a plus and the second one has a minus if you type both of these into your calculator to get them as decimals remember the question asked us for three significant figures this time so the first one would be x equals 2.14 and the second one would be x equals negative 0.468 thank you for watching this video i hope you found it useful check out what i think you should watch next and also subscribe so you don't miss out on future uploads you