Solve the Square Root equation

this is what we call the peel the onion strategy so on a problem like this what we simply need to do is isolate the X it seems fairly basic on this but there's a lot that's happening to this x right we have it multiplied by two here subtracted by four here and then we have the square root of it then it's being multiplied by two and then it's be subtracted by four so to go ahead and solve for x we need to understand how to approach this what we're looking for well when we have a function like a square root or a power or a fraction or a rational function or s or cosine or any whatever logarithm whatever the function may be there's an inside and an outside of that function for the square root or a radical anything that's under that radical is going to be what we call inside of our function so what we're going to want to do focus on first is to isolate that function so right again the square root function is going to be our function we need to isolate it so what that means is we need to undo the two and the four so which one do we choose because a lot of students will make the mistake they'll start reducing these with the X because these are directly impacting the ax and no if you think about an onion right the onion has many layers inside of it and what we want to do is we want to work from the outside all the way in so in this middle here's we have the nice little X all right so what we're going to do is we're going to work on this outside and these are going to be like your operations so the first operation that we always want to be able to do is anything that we have addition or subtraction okay so you can see the first devil here is we have subtraction of 4 so the first thing I'm going to do is add a four to both sides so 5 = a 2 < TK of 2 x - 4 then the next layer is going to be multiplication or division we want to see is there anything multiplying or dividing by our function well in this case we have a two so we're going to go and divide by two on both sides again notice that's two times this function the square root of 2x - 2 so those are only going to divide out so now I'm left with a 5 Hales is equal to a < TK of a 2x - 4 now we have obtained now what we've done is we've isolated our function okay and actually we have one more here so we've isolated the function now what we need to do is understand what is the inverse operation of our function right logarithm exponential we could have a a fraction s cosine there's many many different functions that we can deal with well for the square root the inverse operation is going to be to square both sides so now Square both sides and I'm left with a 25 over 4 = a 2x - 4 now you see I have an X right multiply by two subtract by four so now I'm just going to do the same thing that I did before I'm just going to undo addition and subtraction and then I'm going to undo multiplication division right we're always doing our reverse order of operations now I ran out of space because I was kind of writing too big but that's okay so I always want to add you know four on both sides and then you're left with a 25 over four the main thing I want you to understand is how do you add 25 or four to a four well the main thing you're going to want to do is change your four into a fraction and again to add fraction they got to be the same denominator so if you multiply by a 4 over4 I don't know where I read a division bar there then what that's going to give you is a 16 over4 so now what I have is a 2X is equal to a 16 over 4 plus a 25 over 4 well 16 + 25 is going to be a 41 so 2x is equal to a 41 over 4 now I can undo my multiplication by dividing by two and remember dividing by two is the same thing as multiplying by 1/2 right so therefore I have an X is going to equal to a what was it 41 over 8 hopefully this video was helpful for you if it was then check out the next video I have for you here