Hey everyone. You just finished learning 3 different methods of solving quadratic equations, and you might be wondering how there's anything left and why we have yet another method to learn. But the quadratic formula that we're going to talk about now is really great because it's going to work for any quadratic equation. So even if you were to forget every single other method, as long as you remember the quadratic formula, you're going to be able to solve any quadratic equation that gets thrown at you. So let's go ahead and jump in. The quadratic formula is based on the standard form of a quadratic equation ax² plus bx plus c, and we're going to use a, b, and c in order to compute our solutions. So the quadratic formula is:

− b ± b 2 − 4 × a × c 2 × a .

Now that formula might look a little bit complicated right now and, unfortunately, it is something that you're going to have to memorize. But a way that I was able to memorize the quadratic formula was by using the quadratic formula song. Now, I'm not going to sing it for you right now, but it's gonna be something that you should search up on your own to commit this formula to memory. So when do we want to use the quadratic formula? Well, like I said, you can use the quadratic formula whenever you want, and some clues that you might want to use it are that you can't easily factor or you're just otherwise unsure what method to use.

Let's go ahead and take a look at an example here. So I have x² plus 2x minus 3 is equal to 0. Let's go ahead and take a look at our first step, which is to write our equation in standard form. Now it looks like my equation is already in standard form, all of my terms are on the same side in the descending order of power, so I can go ahead and move on to step 2. Now step 2 is simply to just plug everything into my quadratic formula, so let's go ahead and do that here. I'm first going to label a, b, and c in my equation so so that it's easy for me to just take them and plug them in. So in this case, I have an invisible one in front of that x² and that is my a, b is this positive 2, and then c is negative 3. Make sure that you're paying attention to the signs here. So plugging this in, the result is:

− 2 ± 2 2 − 4 × 1 × − 3 2 × 1 .

Now that we've plugged everything in, we've completed step 2, and all that we have left to do from here is algebra. We're just gonna compute and simplify our solutions now. So let's start with what's in our radical here and just simplify that. So this 2² is going to become a 4 minus 4 times 1 is just 4, so, really, that's just 4 times negative 3. I know that 4 times negative 3 is negative 12, and 4 minus negative 12, this becomes a plus stringByAppendingString,