A Nice quadratic algebra simplification math problem|solve for x

Let's solve this using two methods. Welcome to my channel. Let's get straight to the point. We are going to solve this using these two methods. Now, the first method, which is method 1. We have x plus 7 squared is equal to 25. Now let's move this 25 to the other side of the equation. If we do that, we have x plus 7 all squared minus 25 equals 0. So let's change this to a square. So we have (x + 7) squared minus 25 equals 5 squared, which is equal to 0. Now we have a difference of two squares here. Remember that a squared minus b squared equals a minus b multiplied by a plus b. Now in this situation, you can see that our a is x plus 7 while our b is 5. So if we should substitute this or write it in this form. So it's going to be a minus b, which is x plus 7 minus 5. So write this as x plus 7 minus 5 multiplied by a plus b, which is x plus 7 plus 5. So we have x plus 7 plus 5, and this is equal to 0. Now remember that if a, b equals 0, then a equals 0 or b equals 0. That means we have x plus 7 minus 5, which gives us 2. Multiplying x plus 7 plus 5 gives us 12, which is equal to 0. So, as I just explained, it simply means that x plus 2 equals 0. Either this is equal to 0 or x plus 12 is equal to 0. Now, if we move this to the right-hand side, or transpose it, we find that x equals minus 2. And if we transpose this, we obtain that x equals minus 12. So these are the two values of x obtained using the first method: -2 and -12. Now the second method, which is the most interesting and the one I love most, goes like this. Now the second method states, or we can carry out the second method in this form. Remember that this is method 2. Now remember that, let's bring out the equation first. Alright, so this is the equation. Remember that a plus b raised to the power of 2 is equal to a squared plus 2ab plus b squared. Now, if you look at this, our a is x while our b is 7. So we are going to expand this in this format. So if we do that, we have a squared, which is x squared, plus 2ab, 2 multiplied by x multiplied by 7, plus b squared, which is plus 7 squared, equals 25. So we have x squared plus 2 times x times 7, which gives us 14x, plus 7 squared, which gives us 49, equals 25. Okay, now we have x squared plus 14x plus 49. Now let's transfer this to this side. If we do that, we get minus 25 equals 0. So, have you given us a thumbs up yet? If not, please do so. And kindly follow, subscribe to the channel, and click on your notification bell if this is the first time you're seeing us. Thank you. So back to what we are doing. We can simplify this further to x squared plus 14x. 49 minus 25, 9 minus 5 gives us 4. And 4 minus 2 gives us 2. So this is what we have, is equal to 0. Now we need two factors of 24. When we add these two factors together, we get 14. So the two factors are 12 and 2. So if we say x squared plus, we replace this 14x with 2x plus 12x. And 2 times 12 will still give us this 24. Okay, is equal to 0. Now let us factorize. This is the same as x squared plus 2x plus 12x plus 24. Alright, it is equal to 0. Now, the common term here is x. We bring it out. We have x brackets. When x squared is divided by x, we get x. When 2x is divided by x, we get 2. Besides, the common term is 12. So we bring it out. 12x divided by 12 is x. And 24 divided by 12 is 2. Is equal to 0. So we have the same thing inside the brackets. That simply means this can be written as (x + 2)(x + 12) = 0 Now remember how we solved it the last time. Is x plus 2 equal to 0 or x plus 12 equal to 0? Now, if we transfer this to this side, we have that x₁ is minus 2. And that x squared is minus 12. As easy as that. Now let's prove that the answer we obtained is correct. So our x is either -2 or -12. Either minus 2 or minus 12. So we have minus 2 when x is equal to minus 2. We have negative 2 plus 7, all squared, is equal to 25. Now 7 minus 3 gives us 4. So we have 5 squared equals 25. And you can see that 25 is equal to 25. That is when x equals minus 2. Now when x is equal to minus 12. So when x is equal to minus 12. We have minus 12 plus 7 squared equals 25. Now 7 minus 12 gives us minus 5. So we have minus 5 squared is equal to 25. So this sentence, minus squared, will give us plus. And 5 squared gives us 25, which is equal to 25. So you can see that plus 25 is equal to 25. Thank you so much for watching. I would love to see you in my next video.