A Nice algebra math question| can you solve for x?

Hi amazing friends, let's solve for x. First of all, when you have a divided by b raised to the power of x, this is equal to a to the power of x divided by b to the power of x. Okay, so we are going to express this side in this form. So if we do that, we x to the power of 6 divided by 2 to the power of 6 equals 3 to the power of 6. Now we are going to cross-multiply. If we cross-multiply, we have that x to the power of 6. is equal to this times this, that is 2 to the power of 6 multiplied by 3 to the power of 6. Now remember that a to the power of m multiplied by b to the power of m is equal to ab raised to the power of m. Okay, so that simply means that we can write this as x raised to the power of 6 equals 2 multiplied by 3 raised to the power of 6. So x to the power of 6 is equal to 6 to the power of 6. Now let's transfer this to the other side of the equation. Okay, if we do that, we have x to the power of 6 minus Alright, remember that a to the power of m times n is equal to a to the power of m raised to the n. power of n. Okay, now that means this can be expressed; we can express 6 as the product of its factors. That means 6 can be expressed as 3 multiplied by 2. Okay, so write x to the power 3 multiplied by 2 minus 6 to the power of 3 multiplied by 2 equals 0. Now applying the the law that I just explained, we can write it as x to the power of 3 raised to the power of 2 minus 6 to the power of 3 raised to the power of 2 equals 0. Now we are seeing the difference of two squares. Yes, the difference of two squares states that a squared minus b squared is equal to a minus b multiplied by a plus b. Okay, that means that we can write this as x cubed (-6)³ × x³ + 6³ equals 0. Now we can say that when a multiplied by b equals 0, then either a equals 0 or b equals 0. Okay, so that means we can write that either x cubed minus 6 cubed equals 0 or x cubed plus 6 cubed The power of 3 is equal to 0. Now I want us to note one thing. Remember the algebraic identity that states that a to the power of 3 minus b to the power of 3 is equal to a minus b multiplied by a squared plus a b plus b squared and a to the power of 3 plus b to the power of 3 is equal to a plus b multiplied by a squared minus a b plus b squared. Okay, so we are going to use these identities to expand this one and this one. So let's do that. So if we do that, On this side, we are going to have x minus 6 multiplied by a squared plus 6x. plus 6 squared. Okay, so that means this is equal to 0. Let me shift this a bit, please. So this is x cubed plus b cubed equals zero. Okay. Now this is equal to 0. Okay, then for this side, for this side, we are going to have x plus, this is 6, x plus 6 multiplied by x squared minus 6x plus 6 squared. Okay, This is equal to 0. Okay, now on this side, you can see that x minus 6 is equal to 0. excuse me, x minus 6 equals 0 or x squared plus 6x plus 6 squared equals 0. So if we Look at this; you can see that x is equal to 6. This is the first value of our x. Now for this, So I'm going to copy this part out, alright, because I'm going to solve that. Later. So x plus 6 multiplied by x squared, I know you cannot see this, x squared minus 6x plus 6 squared is equal to 0. So let's solve this first, alright. Okay, so we continue from here. Now here, we have that x squared plus 6x plus 6 squared, I apologize, is equal to 0. Now 6 squared is the same as 36, so let's replace this with 36. Alright, now let us solve this using the quadratic formula and according to the quadratic formula, x is equal to minus b plus or minus the square root of b squared minus 4ac, all divided by 2a. So x is equal the coefficient of x squared is 1, b is equal to the coefficient of x, which is 6, and c is equal to our constant, which is 36. So that means that we can write this as x is equal to minus 6 plus or minus the square root of b squared, which is 6 squared minus 4 multiplied by a which is 1 multiplied by c, which is 36. Everything divided by 2 multiplied by 1, okay. So our x is equal to minus 6 plus or minus square root of 6 squared, which is 36, minus 4 multiplied by 36 everything divided by 2. So if we continue, you can see that x is minus 6 plus or minus Square root of, now 36 and 36 are the same thing, right, so we can factor that out since it's common. So we bring out 36; 36 divided by 36 is 1, minus 4 times 36 divided by 36, 4 remains. divided by 2. So we need to continue from this side of the board, okay. Alright, remember that we have obtained the first value of a as 6, or the first value of x as 6, okay. So we are looking for the second and third, the fourth, the fifth, and sixth values of x. If this is the first have seen us, please click the subscription button, turn on the notification bell so that you Don't miss our amazing videos. We upload our videos every day. So tune in, as you're confident. To watch our new uploads, give us a thumbs up if you're actually enjoying this video. Thank you. That's what we're doing. So you can see that x is equal to negative 6 plus or minus square root of what? Now before this, remember that the square root of a times b is equal to the square root the square root of a multiplied by the square root of b, okay. So this will give us the square root of 36 multiplied by minus 3, okay, divided by 2. So x is equal to minus 6 plus or minus square root of 36 multiplied by the square root of 3 multiplied by the square root of minus 1, okay. Everything divided So our x is equal to negative 6 plus or minus, now the square root of 36 is 6, so we have 6. The square root of 3 and the square root of minus 1, which is i, divided by 2. So you can see that x equals minus 6 divided by 2, which gives us minus 3 plus or minus 6 divided by 2, which gives us 3 root 3, and so these are the second and third values of our x. The second and third value of our x. Now let's go back to what we had before. Remember that we had the one I copied Here, okay, that x plus 6 multiplied by x squared minus 6x plus 6 squared equals 0. So this is What we have, okay. Now x plus 6 from here, x plus 6 is equal to x squared minus 6x plus 6. squared is 36 is equal to 0. So from this side, x is equal to minus 6 as well, okay. So this is the fourth value of our x. Now back to this side, we are going to solve this using the quadratic equation formula that states that x is equal to minus b plus or minus square root of b squared minus 4ac. All of it divided by 2a. Now our a is the coefficient of x squared, which is 1, our b is the coefficient of x is minus 6, and our c is the constant, which is 36, okay. So we have x equals to minus minus 6 plus or minus square root of b squared, that is minus 6 squared minus 4ac 4 multiplied by 1 multiplied by c, which is 36, okay. Everything divided by 2 multiplied by 1. So we have x equals minus minus, which is plus, so we have 6 plus or minus square root of minus 6. is 36 minus 4 multiplied by 36, okay. Everything divided by 2. So if we continue, we can say that x equals 6 plus or minus the square root of, let's factor out 36, okay. So it's going to be 36 divided by 36 is 1, and 4 times 36 divided by 36 leaves 4 remaining, all over 2. So x is 6 plus or minus the square root of 36 multiplied by minus 3, all divided by 2. So x is equal to 6 plus or minus the square root of 36 multiplied by the square root of minus 3. divided by 2. So we continue from here. Therefore, our x, our x, our x is equal to 6 plus or minus The square root of 36 is 6, and we have the square root of 3 multiplied by the square root of minus 1, all divided by 2. So we have x equals 6 plus or minus 6 times the square root of 3 times i, yes, because the square root of minus 1. Is i divided by 2? So if we solve, we have 6 divided by 2 is 3 plus or minus 6 divided by 2. is another 3 root 3 i. So these are the fifth and sixth values of our x. Thanks everyone for watching.