Where the Quadratic Formula Actually Comes From #algebra #math #shorts

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[00:00:00]So let's just treat this like any other quadratic. The first thing I'd do if I was going to complete the square is I would get my C to the other side.

[00:00:07]Therefore, I have a AX squared plus a BX is equal to C. Now when I divide everything by A, I now get the equation of X squared plus B over AX equals a C over A. Now we have something we can create the square with. What is the value that is going to create the perfect square trinomial? So I'm just going to use a little question mark. And remember, whatever we do on the left-hand side, we have to do on the right-hand side. So what I'll do is I'll take my question mark and say that is going to be my middle term, right, divided by two quantity squared. So when I go ahead and take a B divided by a 2A quantity squared, that's going to give me a B squared over a 4 A squared.

[00:00:39]Remember, that's what I'm going to add to both sides. Now you can see I have one variable X, right? And I can just use my inverse operations. So I go ahead and take the square to both sides. And ladies and gentlemen, I now have a formula that I can find any solution to any quadratic. And rightfully so, this formula is called the quadratic formula.