Many get stuck solving this algebra equation.

To find the value of x is not easy, but we can do it together. Welcome back to my channel. So I would like you to grab your popcorn and let's do this together. So first of all, we are going to write 54 as 6 plus 48. Don't ask me why. Just watch and see what I'm trying to do. So, x squared plus 6x plus 48x plus 9 divided by x plus 3 is equal to 14 root x, okay? Now, I'm looking for something that is factorizable, and from here, we can write 6 as 2 multiplied by 3 multiplied by x. I will explain later, okay? Then I'm going to bring this 9 here plus 48x divided by x plus 3 is equal to 14 root x. Now, let me explain. What am I trying to do here? Remember that x plus y all squared is equal to x squared plus 2xy plus y squared, right? So, you can see that we have 2 here, we have 3 here. Alright? 2 times 3 times x. And this can be written as 3 squared. Therefore, I'm trying to bring x and plus 3 in a bracket to get this one. Now, this is what I mean. I have x squared plus 2 brackets 3 multiplied by x plus 9 is 3 squared plus 48x divided by x plus 3. is equal to 14 root x now if you look at this you'll notice that this is in this form all right therefore i can write from here to here as so we can now rewrite from here to here as x plus 3 all squared plus 48 x divided by x plus 3 is equal to 14 x 14 root x rather we have this and we have this so we can actually simplify them so we can say let x plus 3 be equal to m if i make these statements we are going to write this as equation one and i'm writing somewhere so that even when i clean it later from here i will still remember so if x plus 3 is equal to m before we forget or if i forget if this is the first time you're going across my channel please hit the subscription button turn on your notification bell so that you don't miss my amazing videos all right always tune in at your convenient there must be something new for you to watch give me a thumbs up if you actually love this video and let me have your comment in the comment section yes tell me how you feel whether i did well where i made mistakes what you love about my teaching and where you want me to improve as well i will kindly and i'll be happy to see that as well now if we continue it means that x plus 3 is m right so we'll have m squared plus 48 x divided by m is equal to 14 x now let's multiply we have m squared plus 48 x plus this will be 14 m root x okay this will be minus 14 m root x is equal to 0 okay now we have another thing to do we need to break down this minus 14m root x again so we are going to have m squared now write this as minus 6m root x and minus 8m root x then before plus 48x is equal to zero so let's factorize here m is common so we bring out m m bracket m minus this will be 6 root x then here minus 8 root x is common minus 8 root x bracket when this is divided by this we have plus to start with so this is already positive and m will remain then when this is divided by this You are going to have minus 6 root x is equal to 0. Yes, let's multiply. Minus x times minus 6 is plus 48. And root x times root x is x. So we've not changed anything. Now, moving forward, we have that. So since this and this are the same, we can write m minus 6 root x multiplied by m minus 8 root x is equal to 0. Okay? so this means that m minus 6 root x is equal to 0 and m minus 8 root x is also equal to 0 but recall what we talked about our m right let me stand here even though i don't feel comfortable writing because i'm right-handed so recall that our m what i wrote somewhere that our m is equal okay still here x plus 3 x plus 3 so i will replace that for the first one i will now have x plus 3 minus 6 root x is equal to 0 for here i also have x plus 3 minus 8 root x is equal to 0 okay now if we solve for that we can say again because we need to simplify this right so we can say let's root x be equal to n if we say let's root x be equal to n that means we are going to have x is equal to n squared okay all right so we are going to write this as here we have x plus 3 right that means n squared plus three so we have n squared plus three minus six minus six now root x is n six n is equal to zero is equal to zero now for the second part let me write this closer because i need to manage that space so like i said our x is n squared so i'm going to have n squared, plus 3, plus 3, minus 6, minus 6. Now, root x is n, minus 6n, is equal to 0. Then, we have the second one. x is what? n squared. So, we have n squared, plus 3, plus 3, minus 8. Root x is n, is equal to 0. So if we rearrange this, this is now in the form of a quadratic equation. So we're now going to have n squared minus 6n plus 3 is 0. And for the other side, we have n squared minus 8n plus 3 is 0. Now, moving forward, we are going to solve this using the quadratic equation formula, right? that means that our n is going to be minus minus six for this which will be plus six plus or minus square root of minus b squared that is six squared which is same as six squared right minus four ac that is four minus one four times one times three so four times one times three all over 2a, 2 multiplied by 1. The same thing here, our n will be, our b here is minus 8, which is 8, plus or minus square root of b squared, that is minus 8 squared, which is written as 8 squared, minus 4ac, 4 multiplied by 1 multiplied by 3, everything divided by 2 multiplied by 1. Alright, now, if we solve the left, we have n is equal to, 6 plus or minus square root of 6 squared is 36 minus 4 times 3 is 12 divided by 2 and this one will give us n is equal to 8 plus or minus square root of 64 minus 12 divided by 2 so we have n is 6 plus or minus square root of this will give us 24 right yes divided by 2 and this will give us n is equal to 8 plus or minus square root of 4 minus 2 is 2 6 minus 1 is 5 divided by 2 have you subscribed because i believe this is a very interesting math so please and i'm going to write something again remember we said square root of x is equal to n so i'll write this somewhere square root of x is n that means x is n squared so here we have n is equal to 6 plus or minus now this same thing as 4 times 6 square root of 4 multiplied by 6 divided by 2 then for this we have n is equal to eight plus or minus square root of now let's simplify 52 so we go into this to give us 26 so we go into this to give us 13 so i think we have a prime already which is um we have a perfect square already which is four so it's going to be four times 13 four times 13 everything divided by 2 so moving forward we have n is equal to this will be 6 plus or minus 2 root 6 2 root 6 divided by 2 and the other side we have n is equal to 8 plus or minus 2 root 13 2 root 13 divided by 2 so we have that n is 2 we go into 6 3 plus or minus root 6 right i also have n is equal to 8 plus okay sorry 8 divided by 2 is 4 plus or minus root 13 now remember we are looking for the value of x not n but also remember that we said root x is equal to n right that means we have root x is equal to n that means we can replace n with root x right so we now have let me stay like this so we now have root x is equal to 3 plus or minus root 16. So what do we do next? If we square both sides, we have x is equal to 3 plus or minus root 16 all squared. The same thing will happen here. If we do the same thing here, we will have that root x is equal to 4 plus or minus root 13. That means x will be 4 plus or minus root 13 squared we are not yet done but we are almost there so going forward from here you have x is equal to 3 squared is what 9 right plus or minus 2 times 3 times root 16 root 6 2 times 3 times root 16, we give us 6 root 6. Then plus root 6 squared is what? 6. Then for this, we are going to have x is equal to 4 to the power of 2 is 16 plus or minus 2 times 4 times root 13 is 8 root 13 then um root 13 squared is 13 so plus 13 so we can write x to be 9 plus 6 is 15 plus or minus 6 root 6 and from here x is equal to 29 plus or minus 8 root 13 and that is the answer thank you for watching and see you in my next video bye