in-43-46-solve-each-equation-for-the-variable-x281

Question

In $43-46,$ solve each equation for the variable.
$$
x^{2}=81
$$

James Kiss · Accepted Answer

Well, all right. We are asked to solve the equation. X squared equals 81. All right, To do this, we should write. 81 is a perfect square. 81 is the same thing is nine squared. Now that we have perfect squares on both sides of the equation, weaken square root both sides of the equation. Since where roots and squares are in verses, they cancel each other out. So the square root of X squared is X, and the square root of ah, nine squared is nine. No, don&#x27;t forget the square root property that is not just nine. When we square root a positive number, it is the positive and negative value of it. So the square root of 81 is nine or negative. Nine. We&#x27;re gonna write it in set notation. Negative. Nine and nine.

Dilip Paruchuri · Answer

all right. Hey, guys, In this problem, we&#x27;re giving the equation. A square is equal to 1 96 and in this problem there is no stipulation on what a is. So we don&#x27;t know if A&#x27;s positive. We don&#x27;t know if it&#x27;s a negative number. We clearly know it&#x27;s not zero because you&#x27;re squaring and you&#x27;re getting, ah 1 96 so campy zero. But we don&#x27;t know if it&#x27;s positive. We don&#x27;t know it&#x27;s negative, and we&#x27;re being asked to solve for the values of a So, basically, each operation mathematical operation has its opposite. When you&#x27;re dealing with an equation in order, when you have something added to something the way you get rid of that, it is by subtracting it when you have a variable squared. The way you get rid of that with the square is a few square root boat sites, and that&#x27;s what we&#x27;re gonna do as our first test. We&#x27;re gonna take the square root of both sides, and the square root of the left side is gonna we&#x27;re gonna have squared of a squared square root of a squared is just a and then you have the square root of 1 96 Squared 1 96 is also is equal to 14 squared but also equals here negative 14 square. And since we&#x27;re not taking the principal square, because when we say the principal, when I&#x27;ve talked about the principal square root in the previous problems, we assumed the principal square root because a problem gave us the square root. When the problem gives you the square root, most problems ask you to assume it&#x27;s the principle square root. But in this case, we&#x27;re square routing the pro. We&#x27;re square, routing the number in one of the steps of our solution to the problem. So in that case, we can assume that we&#x27;re taking the principal square root. We&#x27;re just taking the square root, and when you&#x27;re taking the square root, you have to consider all possible values off the square root. So in this case, this can either be 14 squid, the 1 96 another 14 squared or negative 14 squared, and when you take the square root of both the values that you get it plus or minus 14. And if you remember what I said in the beginning of this video that we don&#x27;t have any stipulation on a We don&#x27;t know if A&#x27;s positive or negative. This is what I meant. I meant that they can either be a positive number or negative number because both of these values positive 14 and negative 14 make the initial equation a squared equals 1 96 True, and this is gonna be our answer won&#x27;t have multiple answers to this problem. And that is positive. Negative. 14. Thank you for listening, guys. And I guess the one takeaway is that in this step, when we square root both sides, we&#x27;re not taking the principal square root. And that&#x27;s what gives us our multiple value answers. Thanks for listening.

Dilip Paruchuri · Answer

hey, goes so in this problem were given why squared minus 1 69 is equal to zero. This is an equation we&#x27;re being asked to solve for the values of why not make this equation troop? First step we want to get isolate are variable. So our first step is gonna be or add 1 69 to both sides together. Why squared by itself? And in doing so, we get rid of y squared, we get a once we get rid of 1 69 on the left hand side and we&#x27;re left with y squared is equal to 1 69 Now we want to get rid of the squared on the left hand side. So we do that by taking the square root of both sides. When you take the square root of why squared, you&#x27;re just left with why? And when you take the square root of 1 69 you have to think of both of the options that you might get When I say that. I mean that when you take this square root right here, we&#x27;re not taking a principal square root. We&#x27;re just taking the square root. And because of that we know that 1 69 is equal to both. 13 squared and negative 13 square. So when you take the square root of 1 69 you&#x27;re taking a squirt of 13 square or in taking the square root of negative 13 squared. And the values that you get from doing this are positive and negative. 13. So why couldn&#x27;t get equal both positive and negative? 13. And that will make this equation true. And since why doesn&#x27;t have any stipulations, that has to be positive or negative. Both of these values work, and both of these values are correct. So once again, this step is crucial because when you take the square root, we&#x27;re not taking the principal square. We&#x27;re just

James Kiss · Answer

were asked to solve the equation. B squared equals 100. Since we&#x27;re dealing with a perfect square, which you think of writing wasn&#x27;t 100 as a perfect square and 100 is the same thing as 10 squared. Now that we have perfect squares on both sides of the equation, Weaken square. Root both sides of the equations to get rid of the squares. So if we square root both sides, the square root in the square counteract on each side, leaving us with B equals 10. I don&#x27;t forget the square root property when you square root. A positive number is the positive and negative value of that number. So I get to write this in set notation. We have two solutions here. If B squared equals 100 B could be either negative 10 or he could be a little 10 negative or positive. 10

Jake Zanazzi · Answer

better for his next set of problems. There&#x27;s a couple ways that we could do them. Um, so I&#x27;m gonna show you both ways in this first problem, and then I&#x27;ll go back and forth, Um, in the next couple of one&#x27;s using just one, but feel free to use the other one if it&#x27;s easier for you. So the first ways to move this 81 to the other side of the equation and then try to factor it like we&#x27;ve been doing for most of them. So that&#x27;s gonna give us four X squared minus 81 zero. I think you should notice here that difference of squares equation that we&#x27;ve been working with, um, and that you&#x27;ve been familiar. You know, four X Square is the same thing is to x 81 is always a non squared, so that gives us two X plus nine. A few X minus nine equals zero, and so we can see that X is gonna equal. I&#x27;m just gonna write plus, for my less, um, nine halves because that&#x27;s the first way of doing it. Um, you can also try toe just factoring us out by guessing and checking that would also work. The second way is you have this four x squared. He was 81. What if, um, we just divide through by four and then take the square root? So if we divide through before were given, X squared equals e one divided by four. Now, if we just take the squared of both sides were left with X equals plus or minus nine halves. Remember, when you take the square root of both sides of the equation, you have to remember a plus or minus. Um, and these two ways resolving Give us the same answer.

Martha Richards · Answer

Torre has to solve this problem here. So the first thing that I&#x27;m gonna do is they&#x27;re gonna get this 49 on the other side by subtracting 49 from both sides. So I get four ax squared, plus four x minus 48 equals zero. And you can quickly see here that all of these numbers are divisible by four. So you could just divide both sides by four and I get X squared, plus X minus 12 is equal to zero and then cause you were divided by 40 And then when I factor this, I get an X and then I need to find factors of 12. I have a negative here, so I have to have one positive one negative. The positive numbers got to be bigger. And the difference has got to be one, because that&#x27;s what&#x27;s in front. Here is the one. And so then you can see that the factors of 12 that will provide a difference of one is four and three. The positive is bigger. So the four goes here, the three goes here and then we have the solution. Here is a negative for and a positive three because the positive three will make this term zero and the negative four will make that term zero and zero times. Any number is zero.

Problem

In $43-46,$ solve each equation for the variable.…

Problem 43 Hard Difficulty

In $43-46,$ solve each equation for the variable.
$$
x^{2}=81
$$

Answer

$\{-9,9\}$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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$\{-9,9\}$

Algebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry