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Solve each of the quadratics by first completing the square. When the roots are irrational, also give the solutions to the nearest one thousandth.$$\frac{3}{5} x^{2}-\frac{3}{2} x=\frac{7}{10}$$

$$\frac{15 \pm \sqrt{393}}{12},-0.402,2.902$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Campbell University

McMaster University

Lectures

02:42

Solve each of the quadrati…

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01:30

In each of the following, …

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02:12

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02:41

02:04

So we have this quadratic of three fists X squared, minus three halves. X equals 7/10. Now I don't mind fractions. The only thing is this leading coefficient needs to be one in order to complete the square. So that's why I'm going to multiply everything in my and my terms by five thirds. It's okay, as long as you do that to all the pieces. Um, so fives canceled. Three's cancel. So that is true. That's X squared. Now this one's a little bit more difficult to do. The three is to cancel. So look at five halves when we reduce. I'd like to leave a blank right here and then work is pretty similar on this one. Only difference. Maybe you look at that and say, Well, five goes into 10 twice, so that would be reduced to 7/6, because three times two is six. Um, you might multiply this out in a slightly more difficult process, but that is correct. So now that we have our leading coefficients one we can do the process of taking our B value, find half of it, and then square that number. That's always the process on completing the square. So we're looking at negative five Force squared. Well, negative times. Negative. Positive. Five squared is 25 four square. It is 16. So I also need to add that same value to this side. So now I'm ready to factor the perfect square, trying to me on the left side and the shortcut. It's always this number. So we're looking at X minus five. Force squared and on the right side. That's kind of ugly. Um, I don't know the easiest for, um, for students to to add them, but I'm just using a calculator. 76 plus 25 16th gave me 131 over 48. You can double check my arithmetic from there to there. But now what I can do is I can square root each side. I don't know the square 131 but I do know. Uh huh. Route 48. That's equal to route 16 times, Route three. That's almost a perfect, uh, ration number. I just need to multiply top and bottom by route three. So now what I'm looking at is the left side is X minus five force. Is that cancelled? 131 times three is 393. And then the denominator. I know the square to 16 is four and three times three is three. Four times three will give me 12. So while I'm at it has to change the left fraction to be the same denominator. So if I multiply that by three, there will be 15 12. So to solve for X, I need to add that term over with the denominators being the same thing. I'm good. 15 plus or minus. Route 3 93 all over 12 is the correct answer. Now, if you also go to calculating typed in 15 minus all over 12 and 15 plus all over 12, you'll get the decimal approximations rounded to three decimal. Yeah, negative. 04022902 Are your irrational answers.

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