Choosing a Method to Solve Quadratics - Video Tutorials & Practice Problems

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Choosing a Method to Solve Quadratics

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So you've just learned all possible methods of solving a quadratic equation. 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. 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. And here I'm going to use that information to show you exactly how to choose method is best. Now, it's important to note here that multiple methods may work for any given quadratic. 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. So let's go ahead and get started. So in our table here, we're going to look at our use if column and a structured way to go through. This is to start with factoring and go go through each method until you find one that matches up with your quadratic equation. 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. But let's go ahead and start with some structure. 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. So taking a look first at my factoring box, let's check if any of this criteria matches. So it either has obvious factors or C is equal to zero. Now, here I do have C equal to zero because I have no constant. So I can actually stop here because I know that factoring is going to be the best method to use. 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. Let's again, start with our factoring box. 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. So factoring is not going to be the best choice here. So let's move on to the square root property. So does it have this form X plus sum number squared equals a constant? No, and is B equal to zero also no here because I have a B of six. So I'm not going to be able to use the square root property either let's move on to completing the square. So is my leading coefficient one and is B even. 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 that tells me that completing the square is going to be the best choice to solve this one. So let's look at another example here. So we've been able to kind of go through each of them and see which one works. Let's take a look at one more. So here I have X plus two squared equals nine. 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 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. So here the square root property is going to be the best method. So now we just have one more left. Let's take a look. So I have two X squared plus seven X plus three equals zero. Let's go ahead and go through left to right one more time. So does this have obvious factors? Well, definitely not and C is not equal to zero, it's equal to three. So I'm not gonna want to factor here moving on to the square root property. It definitely doesn't have, have this form X plus a number squared equals a constant. And I do have a B because I have this seven X. So not the square root property either. And completing the square, is this going to be the best method? Well, my leading coefficient is not one. So the, the completing the square is already out of the picture which just leaves me with the quadratic formula. So that is going to be the best method here. So remember again, multiple methods can work for any quadratic, but these are the best ones. And that's how to choose the best method for any given quadratic equation. Let me know if you have any questions.

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Problem

Problem

Choose and apply the best method to solve the given quadratic equation.

$x^2-6x=5$

A

$x=6+\sqrt{14},x=6-\sqrt{14}$

B

$x=10,x=-4$

C

$x=3+\sqrt{14},x=3-\sqrt{14}$

D

$x=6,x=0$

3

Problem

Problem

Choose and apply the best method to solve the given quadratic equation.