A complicated algebra math challenge.

looks impossible, but with the right approach we get The answer: Welcome back to my channel, first. This thing is over one, and we can cross multiply. And if we do that, we will have x equal to 5. x plus 1 is equal to 1211 multiplied by x squared plus x plus 1. Now let's transfer this This to this side and this to this side as well. so we are going to have x to the power of five is equal to one thousand we are opening this bracket now one thousand two hundred and eleven x squared then this time this will give us plus one thousand two hundred and eleven x plus this time This is one thousand two hundred and eleven. Now I'm bringing this to this side. so we are going to have minus x minus one Please subscribe to my channel and turn on your notification bell. so that you keep seeing these Amazing videos, all right, we upload our videos Tune in as often as possible at your convenience. There must be something new for you to watch, give us a thumbs up if you love what we are doing and Most importantly, always leave your comment, the good The bad, the ugly—we're here to read them all. Provide us with your suggestions, and they will be implemented. Thank you very much so here we have x to the power five is equal to one two one one x squared right one one x squared one thousand two hundred plus one and eleven x minus x is one thousand two hundred and ten x one thousand two hundred plus one and eleven minus one is one thousand two hundred and ten Now I want you to look closely. Because one thing about math is being so observant—now look at this. We have 1210, 1210. Is there anything we can do? Do this to get 1210, yes, we can actually rewrite this. Let's decode 5 equal to 1,210x squared plus x squared, right? Then plus 1,210x. plus one thousand two hundred and ten now looking At this, we have this; we go to the other side, so we x to the power of five minus x to the power of two is equal to one thousand two hundred and ten x squared plus one thousand two hundred and ten x plus one thousand two hundred and ten We can factor out x squared from this side. So we have... x squared brackets when this is divided by this we are left with x cubed so we have x to the power of three minus When this is divided by this, we have one, all right, minus one. is equal to one thousand two hundred and ten x squared plus one thousand two hundred and ten x one thousand two hundred and ten Okay, minus x, okay. If we solve for that. Remember that a to the power of 3 minus b to the power of 3 is equal to a minus b multiplied by a squared minus ab plus ab plus b squared, okay? So, you can actually express x to the power of 3 minus 1 to the power of 3, right? Because 1 to the power of 3 is still 1. So, you can actually express this as x to the power of 3 in parentheses, x cubed minus one to the power three for the left hand side is equal to 1210 times x squared plus 1210x plus 1210 then we expand in this form So we'll have, let me extend My hand a bit, all right. so we have x to the power of two brackets and this will give us x minus one multiplied by x squared plus 1 times x, which is still x plus 1 squared Which one is equal to this, right? 1210x² + 1210x + 1210 Now it's high time, let's expand. this and factorize this side So we have So 2 9 2 2 1 2 2 1 2 9 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 0 x squared times x is x to the power three and x squared times minus 1 is minus x squared (x² + x + 1) is equal to Now we are going to factorize 1210, okay. so we have 1210 (sorry, this concept) This will be x squared plus this times this, and this x will remain. Plus this into this one, are you seeing anything we have? this and we have that amazing Right now, let's transfer this to this side. so that we can factor out this common factor, we have x x cubed minus x squared brackets x x squared plus x plus one minus one thousand two 210, open bracket, this, right? x squared x plus 1 is equal to zero; now we can factorize this, so if we do that we have x squared plus x plus one open brackets so this will remain when this is divided by this, we have this remainder, x to the power of three minus x squared then When the entirety of this is divided by this, we obtain this. Minus 1210 is equal to 0 if you have not subscribed up to this moment That means you were carried away. By how this is being done, it's interesting, right? So please, it's It's time for you to, um, actually subscribe to the channel. so that you don't forget, I don't want to miss my next video all right okay so from here we can see that we can say that x squared plus x plus one equals zero and x cubed minus x squared minus 1210 and 10 is also 0. Now, for this side, we can solve for x, If we should use the quadratic formula, right? If we use the quadratic formula, Our a is 1, our b is 1 as well, and our c is 1, okay? So, using the quadratic equation formula that states that x is equal to The quadratic equation formula states that x is equal to minus b plus or minus square root negative b plus or minus the square root of b squared minus 4ac, all divided by 2a. So if we substitute, we have x is minus 1 plus or minus the square root of 1 squared minus 4 multiplied by Remember, our a is also 1, our c is also 1. Everything divided by 2, multiplied by a, which is 1. So we have that x is equal to minus 1 plus or minus the square root of 1 squared is 1. 4 times 1 times 1 is still 4. everything divided by 2, remember that we will still solve this and we are going to get more values from here, so watch the end and see how we obtained additional values from this side Now let's continue, so I'm going to copy this out. because we are solving it next x to the power 3 minus x squared minus 1210 equals 0 We're almost there, okay? So now we have our x to be equal to minus one plus or minus square root of negative three divided by two this implies that x equals minus one plus or minus square root of three i divided by two, that is because minus three is the same thing as three times negative one and the square root of minus one is i Alright, yes, the square root of minus one is i. and that's where this i comes from, root three and the square root of minus one, so from here you can see that we have obtained the first and second values of our x One and two—that's one. Now let's continue. with the other roots that with the other the equation we have now The other equation I copied down says x equals three minus x squared. minus one thousand two hundred and twenty-four equals zero then we have x to the power of three minus eleven x squared plus ten x squared minus one thousand two hundred and ten is zero So if we factorize this here, we have x squared remaining, right? or as a common factor, then x cubed divided by x squared We have x minus eleven x squared divided by x squared, which is still eleven. plus here we have 10 then x squared divided by 10 we x squared then minus one two one zero divided by this we have minus one times two plus one is equal to zero so here we have x squared brackets x minus 11 plus 10 times the square. Now look at these two brackets; they are similar. because 121 is the same thing as 11 squared, we already have 11 here so we have minus 11 squared is here now remember that a squared minus b squared is equal to a minus b multiplied a plus b, therefore we can now write this as x squared, brackets, x minus 11 x plus 10 into x minus 11 multiplied by x plus 11 equals zero so if you look at this and this They now have x minus 11 in common. and we are factoring that out, so we have x minus 11 into For this side, x squared will remain; for this side, 10. into this will remain 10 brackets x plus 11 Equals 0. So, we have x minus 11 x squared plus 10 times x Is 10x plus 10 times 11 equal to 110 equal to 0? Are you still there? If you are, thank you very much. ❤️ For me, that would show that you actually watched up to this point, okay? so let's confuse those who Didn't watch to this point, just one heart emoji. Thank you. Now looking. At this, we have from here that x minus 11 equals 0 x squared plus 10x plus 110 equals 0. If we solve for that I want to make sure this is clear. now if we solve for that, we can see that x equals 11, so this becomes the third value of our X now for this we are going to solve using the quadratic formula as well so where a is 1, b is 10, that is the coefficient of x and c is a constant, so if you use the quadratic quadratic formula x will be minus 10 plus or minus the square root 10 squared minus 4 multiplied by 1 by 1 1 0 right 480 all over 2 multiplied by 1. So, if we continue, we have x equals minus 10. plus or minus square root of 100 minus 440 everything divided by two, okay, now moving forward we have x equals minus 10 plus or minus the square root of minus 340 divided by two, can we Factorize this 340. Let's check if we can reduce it. to a simpler form so we go through this 170 times So we go into this 85 times and Okay, five, we go into this one, one, okay. I think we We've gotten what we wanted: four and eighty-five. Four is a perfect square. so we can now write x to be minus 10 plus or minus square root of four times 85 times negative one because of the negative sign, now everything divided by two, so x equals negative 10 plus or minus now the square root of 4 is 2 We have 2 root 85 and square root of negative 1 is i divided by 2, so our x which will be the fourth and the fifth value will be 2; we go into this minus 5 plus or minus, we go into this one, so we are left with this square root of 85 I thank you so much for watching See you in my next video, bye