6. [-/1 Points]DETAILSLARLINALG8 2.3.057.Find A_5 ~2 -4 2(3A)-1 =A =...

Solve using the quadratic formula. $$\frac{1}{6} u^{2}+\frac{4}{3} u=\frac{5}{2}$$

Solve this equation here needs a multiply both sides by the LC, which is going to be 12 8 Case of the left side, that is now three a minus plenty. It is equal to sow the rice sight that is. Oh, so you get naked of seven A on the left, 12 on the right. Divide both sides by negative seven and we end up with a is equal to negative 12/7. So now it is up to check your answers. We have 1/4 minus 5/6. No, we didn't check whether we're not that is equal to one over. Make it a total percent. Okay, so the right side we can simplify that. That is negative. 7/12 and then the left hand side. You need to put it over common denominator. So you've been in need to multiply the first traction, like over three. 2nd 1 by two. Over too. And then that's going to give us 3/12 minus 10/12. And that iss naked of seven 12. So you get both sides are native, 7/7 over 12. So that means, uh, a equals negative 12/7 is a solution to the original creation

Let's fill in the blanks here. So we have this complex fraction times when you were 28 solutions a 28 distributor to both of the fractions on numerator. I know that this is going to be 20 a year and 28 years old. Same thing with the denominator because it also multiplied it by auntie. So now what's going to happen as we're going to do with the patient? So we have one of the five times 20 able just for a We have won over eight times. 20 day. That's going to be Thank you. We have a over four times 20 eh? No, that is going to be five glared and then we have to over eight times 28. So this is going to be 40.

The question is is that we have to find a square minus five way plus six i. F A. Is a matrix with the element to +01 213 1 -10. Now, moving towards the solution first, we will be finding Air square which will be given by in two way. So it will be 201 2, 1, -10. into the similar metrics which is 201, 2, -10. And the resultant matrix will be equal to 5 -1, 2, 9 -2, 5 0 -1 -2. Now, moving further, we will be finding developed for five. So five into the A matrix which is 201213 minus 1 -10. So you will get 10 05 10 5, 15, 5 -50. As the resultant metrics. Now we will be finding six side. Now, as we know that i is the identity matrix. So six into the identity matrix which is 100010001 So it will give us the Matrix says 600 060006. No, we will be putting Davies Micros is in the question a square minus five plus six. I so you will get A square is my tracks with the element 5 -12, 9 -2, -1 -2 -5 Way, which is 10 05 then 5 15, 5 -50 plus six side, which is 600 060006. So solving this, you will get your answer as 1 -1 -3 -1 -1 -10 -544. And so this will be the solution to the question. Thank you.

So, in order to solve my quadratic formula with the quadratic no sorry quantitative equation with the quadratic formula, I have to put this in standard form. So the first thing we're gonna do is I'm gonna subtract five halves from each side. I'm gonna be left with 16 you squared plus 4/3 U minus five house. And so now I'm going to out equals zero. So now I write my A B and C values. So the coefficient of my square turn is one sex. The coefficient of my linear term is 4/3 and my constant is negative five house. And I'm gonna write the quadratic formula because that's what we're going to use to solve it next equals no, you're that b plus or minus the square root B squared, minus full, racy all over two A. Yeah, I sang it to the pop goes the weasel And I promise you'll thank me for because you'll never forget it now And I'm gonna substitute my values X a cause indicated being personalize the square the square lines for oh, swoon Oh, over to a rights And I'm going Teoh simplify Not simply, I evaluate. Um do the operations, so we have negative 4/3 plus or minus. The square root of 4/3 square is 16 nights minus. Well, we'll have. This will really be like 4/1. So say that I'm making that for over one so that I have four times one times five, which is 20 over one time sixteen's, too, which is 12. But this isn't negative, so we have subtracting a negative, which is really adding a positive overall, I don't put a in you right and two times one sex list line is like, Ah, I still work with that. OK, let's try. Here we go. So two times 1/6 is 26 which is equivalent to 1/3. So this WAAS 26 is equivalent to 1/3. So that's what that 1/3 came from. I did to tens 16 I got to six and then I divided by two and got the common factor and got 1/3. So now don't do that. Go now we get to do some fun with fractions to me like a television segment. Kids show fun with fractions art, so I want to be able to add my discriminative. So I am going to do local side. Step over here and go and say OK, 16 nights I was 20 12 24 36 So my common denominator is 36. So nine times four is 36. Some of the multiplied by four on my four and 16 times four is 64 plus 12 times three is 36 Tony times various 60. So I get 100 24 over 36. Now, I can simplify that. Um, I know they're both going to be divisible by four. So we're divided by 4 May have to divide by something else. It may have something else in common. So that will be 31 over nine. Well, 30 ones prime, so they don't have anything else in common. Um, Sue. Now I'm gonna put that back in here. X equals negative 4/3 plus or minus the square root most 31/9 over one third. Okay. Now. Okay, Now I'm going to factor out a perfect square here, so this is really, like one nice times 31 over 1/3. So I'm gonna move this down because it's a long all right, so I can factor out the square root of one night. The square root of 1/9 is one clerk. So 1/3 radical. 31 over one third. Okay, so, um, couple ways I can do this. Okay, So here's what I'm gonna do. I'm gonna split these up. Negative. 4/3 over 1/3 plus or minus 1/3 Radical. 31 over 1/3. Well, my friends, the fraction bar represents division. So really, what I'm saying is the X equals negative 4/3 divided by 1/3 plus 1/3 radical 31 divided by 1/3. Now, dividing by a fraction is the same thing is multiplying by its reciprocal. So what this is also telling me is that I could actually write this as negative 4/3 times the reciprocal of 1/3 which is three or 3/1 plus one radical or 1/3 radical 31 cells, right, 1/3 radical, 31 times. The reciprocal of 1/3 which is 3/1. And that I can simplify to three. Divided by three is one. So I am left with X equals, if negative for over one, which is negative for? Oh, and this is plus or minus. Here we go. Plus or minus minus the measure. I wrote a three there again. Three divided by three is one. So we get radical 31/1, which is just radical 31. And all of a sudden it goes from this really yucky looking, crazy, complex fraction mess to the super beautiful it, sir. So X can be We're Yeah, negative. Four plus. So you know what? I'm Sergeant read his There's there's no other close. So extent. Equal negative for plus radical 31 or negative for minus radical 31. So in solution set for its this.