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Solve by factoring.$$3 h^{2}+17 h=-10$$...

Question

Solve by factoring.$$3 h^{2}+17 h=-10$$

Solve by factoring. $$ 3 h^{2}+17 h=-10 $$



Answers

Solve by factoring. $$ 3 h^{2}+17 h=-10 $$

Okay. Looks like here you've been given the task of a little bit of a factoring review. So I'm gonna rewrite my expression and start thinking about how to approach this. So the steps to approach this is First, you look at what we have in your book shows this and we see ask ourselves if we can get a greatest comfort factor. Well, there is no greatest common factor that goes into each of these. I do notice that this has a negative in each of these terms, and it's easier for us to think about the factory's ation. If you factor out a negative one. Have a put on the one here. Actually, um, factoring that out, that gives us all positive values. That just makes it a little easier for our brains to process it. So I got four k squared and that's a five K J and A plus J squared. Now it looks a little bit easier. S O. I think we're gonna need to have here is we're going to have to think of two numbers that multiply to what we want. So, um, we need to have a four. So to get to four. We never two in a two or a one and a four. So I went to the back end of this. First we know the back end is gonna be easier to see. Have a J A. J here because we took all the negatives out the plus in a plus. So, uh, since we need to have add up to five and we'll play before I'm gonna use the combination that gives us the four and the one. So just do a four K and another one k here. And so it would have four k squared plus four KJ plus one KJ, which gives us a total of five KJ and plus the J squared and the negative ones along for the ride. I'm gonna teach turning back toe original color. And if I multiply that out, I get back to the same place where I started. So that's the factories

Okay. Okay for this problem, We were asked to solve this quadratic formula frenetic equation with the quadratic formula. So let's right what we're given. First of all, I'm not gonna write exactly as is if you read your text book. It says three h squared. Oh, actually can like this one, as is three each weird last two age plus negative six. The reason we can like this as it is, is because we know what's in what's called standard form. Okay, so standard form means it's already in the formats. So we know what the A and the B in the cr's. Our first step is we're gonna write down a B in the sea that we're gonna substituted into the quadratic formula, and then we're going to simplify to solve it. So first thing first, that's right down our are coefficients. So a equals three b equals two negative to just be careful that you, uh, get this negative sign with the the number there in same thing for the sea C equals two negative six and then we're going to do is we're gonna write down the quadratic formula already down this one time, so x equals negative B plus or minus the square root of B squared minus four A c however, to a and then we substitute. And I'm gonna started green for the simplify steps. So right, you're variables, right? Your formula and simplify, substitute and simplify. So we have a negative of a negative too, plus or minus b squared So that negative too square minus four times a times C. So if this guy's a little bit of home So the biggest, most important thing to be to do here just be careful there. Positive and negative signs. Yeah, that's why I have my students use parentheses in fairly clearly put in with the have there. It's a negative negative to its positive, too, plus or minus because we have up the two solutions. Uh, let's simplify This two squared is four, and then we have, ah, negative negatives. That's gonna be a positive result to four times three is 12 12 times six is 72. So overall, we're going to have all right into steps here. Four plus 72. Well, there were six. Next one about is two plus or minus squared of 76 over six and Finally, your teachers usually expect you to simplify if you can. Now, this guy right here, you always want to break it down. The simplest radical form. Um, I know after the side that Ah, 19 temps for 76. So since 19 temps for 76 I can think of this skirt of 76 as a square of 19. Yeah, Ford stopped working here for a second 19 times a squirt of four. So what happens? It's too radical. 19. So I just did this after the side, so you can see it there. So where you see that 76 eso that's going to turn into two radical 19 um, jokes to plus or minus two radical 17/6. And this is what trips up some students. Sometimes you gotta simplify if you can. So since two goes into itself and also into sixth, we're going to simplify each of those down there. So in the end, we end up with the one plus or minus radical 19 over three that your final answer and your teach male like it just like that. Um, and the textbook may say, or sometimes usually put in decimal form as well to. So that's the same as negative one 0.1 to approximately since rounding and 1.78 So, depending on how your teacher wants you to answer it, there's the perfect simplified form, and there's the decimal approximations.

First thing we need to do is we need to get this fraction alone. So we're going Thio. Subtract 10 from both sides like a H over three, this sequel to negative nine. Now we need to get the H Alone's when you need to multiply both sides by three, and that gives me ages equal to negative 27.

All right. So you were given there, quadratic that we just have to factor this one. Um, isn't you hard? Because there aren't that many, uh, possible things to try, since one is a prime number. Um, you know, it's gonna have to be one of one. And we know since all the signs of positive, it's gonna have to be positive and positive. And remember, you have to double check it. Sometimes, later on, we're gonna have quote Rex that we're not able to factor. So you just foiled this out to double check. It will work, and this is gonna give us Each equals negative one. This is also the same form as the last problem we worked with Where you have a plus B squared equals a squared close to a B plus, be swayed. So if you recognize that, you can factor it even faster. Um, if not, though,


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