solve each equation with the quadratic formula

#Solve each equation with the quadratic formula how to
#Solve each equation with the quadratic formula plus

In this case, you will add 1 because it perfectly factors out into (x-1)^2. Next, you want to add a value to the variable side so that when you factor that side, you will have a perfect square. Because there is a 3 in front of x^2, you will divide both sides by 3 to get x^2-2x=5. Next, you want to get rid of the coefficient before x^2 (a) because it won´t always be a perfect square. To do this, you will subtract 8 from both sides to get 3x^2-6x=15. To complete the square, first, you want to get the constant (c) on one side of the equation, and the variable(s) on the other side. Let me know if you have any questions.You don´t need another video because I´m about to explain it to you! Say you have the equation 3x^2-6x+8=23.

#Solve each equation with the quadratic formula how to

And that's how to choose the best method for any given quadratic equation. So remember again, multiple methods can work for any quadratic, but these are the best ones. So that is going to be the best method here. So the, the completing the square is already out of the picture which just leaves me with the quadratic formula. And completing the square, is this going to be the best method? Well, my leading coefficient is not one. And I do have a B because I have this seven X.

#Solve each equation with the quadratic formula plus

It definitely doesn't have, have this form X plus a number squared equals a constant. So I'm not gonna want a factor here moving on to the square root property. So does this have obvious factors? Well, definitely not and C is not equal to zero, it's equal to three.

Let's go ahead and go through a left to right one more time. So I have two X squared plus seven X plus three equals zero. So here the square root property is going to be the best method. So I have X plus A number squared is equal to a constant, which I know is one of the clues that I should use the square root property. Now this is an example of a quadratic that we're gonna be able to look at and know exactly what me to use because there's such a specific thing happening. So here I have X plus two squared equals nine. So we've been able to kind of go through each of them and see which one works. So that tells me that completing the square is going to be the best choice to solve this one. Well, I do have a leading coefficient of one because that X squared is just by itself there and B is six, which is an even number. So is my leading coefficient one and is B even. So I'm not gonna be able to use the square root property either let's move on to completing the square. Also know here because I have a B of six. So does it have this form X plus some number squared equals a constant? No, and is B equal to zero. So let's move on to the square root property. So factoring is not going to be the best choice here. So does this have obvious factors or is C equal to zero? Well, it doesn't have obvious factors to me and I do have a constant, I have this one. Let's again, start with our factoring box. So let's go ahead and take a look at our second example here I have X squared plus six X plus one is equal to zero.

So I can actually stop here because I know that factoring is going to be the best method to use. Now, here I do have C equal to zero because I have no constant. So it either has obvious factors or C is equal to zero. So taking a look first at my factoring box, let's check if any of this criteria matches. So looking at our first example here, we want to choose which method is best and I have X squared plus three X equals zero. But let's go ahead and start with some structure. Now, as you get more practice, you're going to be able to just look at a quadratic and you might be able to see right away which method it matches up with and that's fine as well. This is to start with factoring and go go through each method until you find one that matches up with your quadratic equation. So in our table here, we're going to look at our use if column and a structured way to go through. But here we're going to be focused on choosing which one is best, which one is going to make our quadratic equation, the easiest and most straightforward to solve. Now, it's important to note here that multiple methods may work for any given quadratic. And here I'm going to use that information to show you exactly how to choose method is best. But how do we know which method is best for any given quadratic? Well, we've been collecting information on when we should use each method.

But that means that you can just be given a quadratic equation with no direction on what method to use and just be expected to choose the best one.

So you've just learned all possible methods of solving a quadratic equation.