Everyone gets X=5 but is that really the answer?

Can you find all values of x? All values of x? Welcome back to my channel. Do you know that we have six values of x and some of us we make the mistake of solving it this way. x to the power of six is equal to five to the power of six. This implies that x equal to five. So where are the other five values of x? Welcome back to my channel. Now let's dive into the show of today. So we are asked to find all values of x. None should be left behind. And this is the best way to do it. Like I did, this x to the power of six is equal to, now this is actually five to the power of six. So that line is very correct. But this is what you're supposed to do in order to avoid getting only one value of x instead of six. So we are going to transfer this to this side and we have x to the power of six minus five to the power of six is equal to zero. Now this is where the knowledge of algebra, exponents comes in. So we go on from here. We need to note that six is equal to two multiplied by three. So we can actually write this as x to the power of two raised to the power of three minus five to the power of two raised to the power of three. Okay. Note, this won't give me what I want. Let's do it this way rather. Let's do it this way. x to the power of three raised to the power of two. So I'll use difference of two squares minus five raised to the power of three raised to the power of two. Right. Now this is zero. Now recall that a squared minus b squared is equal to a minus b multiplied by a plus b. Okay. So in this case, a is equal to x to the power of three while b is equal to five to the power of three. So that simply means that we can now write this equation as x to the power of three minus five to the power of three multiplied by x to the power of three plus five to the power of three is equal to zero. Please subscribe to my channel and turn on your notification bell. Yes, if this is the first time you have seen this lovely and wonderful channel and personality. Yes, don't mind me. Sometimes I'm so unserious. So if this is the first time you have seen me and this lovely channel, hit that subscription button and ensure your notification bell is turned on so that once I upload any video, you'll be among the first to be notified. All right. Give us your comments. Very important in this channel. Tell us how you feel about the videos. Give us your suggestions. They are highly appreciated. Okay. Now back to what we have on the board. We have that. Remember this algebra identities. The one that says that a to the power of three minus b to the power of three is actually a minus b multiplied by a squared plus a b plus b squared and a to the power of three plus b to the power of three is equal to a plus b brackets a squared minus a b plus b squared. So that means that here from this equation, note that this can be written as x to the power of three minus five to the power of three is or x to the power of three plus five to the power of three is zero. Now we are going to take this. If we take this, the x to the power of three minus five to the power of three is zero. We can expand it in this form as x minus five into x squared plus five x, right? Plus b squared. That is five squared, which is 25 is equal to zero. So from here we have x minus five is zero and we have x squared plus five x plus 25 is zero as well. So moving forward, we can see from here that x is equal to five. We have gotten the first value of x. Now we're going to write a survey that x is equal to five. Now for the second value here, excuse me, you can see that a is one, the gradient of x grade. B is five, the gradient of x. C is 25, our constant. Now solving for that, therefore solving the seasonal quadratic equation formula, x will be equal to minus b plus or minus square root of b squared minus four a c all over two a. So we have x is minus five, right? Plus or minus square root of b squared five squared minus four multiplied by a, which is one. C, which is 25. Everything divided by two multiplied by a, which is one. So we have x is minus five plus or minus square root of 25 minus four multiplied by 25. Everything divided by two. So we have x is equal to minus five plus or minus. Now if you look at here, we have 25, we have 25. Let's factorize that out. So 25 comes out bracket. When 25 divides itself, we have one minus. When four times 25 is divided by 25, four is remaining. Everything divided by two. Now this is a call to remind you that you have forgotten to subscribe. Yes, you have forgotten to subscribe. So please go ahead and subscribe, okay? I think I've cleaned something I'm not supposed to clean. The one we solved here is x to the power of three minus five to the power of three, right? And we are going to solve x to the power of three plus five to the power of three. Let me write this somewhere. Is equal to zero. Okay. All right, now I'm still waiting for you to subscribe. Okay, let's continue. So from here now we have our x to be equal to minus five plus or minus square root of 25 times negative three, right? So we have square root of 25 multiplied by negative three. Everything divided by two. x will be equal to negative five plus or minus. Now you can split this as square root of 25, which is five, and square root of negative one, which is i, and we have three. So it's going to be three, sorry, it's going to be five root three i, right? Because square root of 25 is five. Then we have root three. The square root of negative one is i. Now divided by two. So from here you can see that we have gotten the second and the third value of our x here. Now let's look for the rest. So recall when we said that x to the power of three plus five to the power of three is zero. I mistakenly erased it, but this is the one we have not solved. So this can be expressed as x to the power of three plus five to the power of three is actually equal to x plus three, x plus five, sorry. Okay. Multiplied by x squared minus five times x, right? Then plus five squared, which is 25. Now everything is zero. All right. Now let's continue. We have x plus five into x squared minus five x plus 25 equals zero. I'm writing this more clearly. So from here we can see that x plus five is zero, which implies that x is negative five. So we have gotten the fourth value of our x, remember. Now for the remaining one, which is x squared minus five x plus 25 equals zero for this one. Remember that our a is going to be one, our b is going to be negative five, this one, and our c is going to be constant plus 25. So we have a is one, b is negative five, c is 25. So if we solve this using the quadratic equation formula that says that x will be minus b plus or minus square root of b squared minus four a c all over two a, we can write that x is minus minus five because our b is negative five, plus or minus square root of minus five squared minus four multiplied by one multiplied by, our c is 25. Everything divided by two multiplied by one. So our x will be minus minus is plus. So we can write this as five plus or minus square root of, this is 25, minus four multiplied by 25, everything divided by two. We're almost there. The answer is just a few steps ahead. So we can now write the x, remember we have gotten four values of x. So x is five, plus or minus, then here we have 25 and 25 again, we factorize. So square root of 25 bracket, 25 we go into itself, one minus four times 25 divided by 25, four remaining, everything divided by two. So x is five plus or minus, now square root of 25 is five. Then we have one minus four is negative three, just like in the previous one. So it's going to be still root 3i, everything divided by two. And this is the fifth and sixth value of our x. Thank you so much for watching and see you in my next video. Bye.