ACT 2: Determining a Solution to a Quadratic

Added: 2026-05-03

[00:00:00]Hello and welcome. So our question today has  which of the following is one of the solutions to the equation. So 'is one' that might mean there  are more than one solutions but there's only going to be one of those solutions inside of the list  that we're given. So let's dive right into it. So for this equation we have an n squared. As soon  as we see that square that means that what we're looking at is what we call a quadratic. Now a  quadratic has a couple of ways you could solve for this thing. You could solve it by factoring.  You could solve it by completing the square.

[00:00:38]You could solve this by quadratic formula.

[00:00:45]Okay. Now there's a there is a fourth method to  solving but in this particular case it's not going to apply. So for this problem there's going to be  three methods of solving. Now between you and me I find factoring to be the fastest for quadratic  so I'm going to use that one but just know there are two other methods in which you could use.  All righty. So for factoring the first step to any factoring problem is going to be GCF right.  Always check for GCF before you go any further in the problem. And right now we only have two  terms. We have an n squared and a negative 81n. What do they have in common? Anything?  Well as it happens they just coincidentally have an n in common right. This first one has  two n's from an n squared. This one has one n.

[00:01:34]They both share an n. So if we pull it out for  the two n's one's going to be left minus 81 because the n um here will just be pulled  out and there'll be nothing left equals zero.

[00:01:47]At this point you'll also hopefully notice that  everything is factored. There's nothing more for us to do here because you have no more powers  larger than one which means you couldn't factor this even if you wanted to. So then you set each  factor each variable uh to zero. So you say all right so first one n equals zero. There's nothing  more to solve there. N equals zero is a solution.

[00:02:10]Your next one is you have n minus 81. We set that  to zero. Well if we want to get n alone adding 81 to both sides we'll do the trick. N equals 81.  And you'll notice that 81 is on your list of solutions. 0 is not but that's okay because 81 is  and that would be your answer to this problem. Now common uh common errors for this one is hopefully  maybe you notice that this is very very similar to what we call a difference of squares. A difference  of squares would be n squared minus 81. If that n was not there then that means that you would have  two factors. You had to have n plus 9 and n minus 9 which means 9 and negative 9 would have been  your solutions right. If you set your n minus 9 equal to zero nine is a solution and n plus 9  equals zero negative 9 is a solution. And you'll notice that both of those are on your list. Okay.  So be careful because that little n was there. The GCF was the way to go and 81 became a solution.  All righty. Thank you so much for watching.