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Find the unknown.$$\frac{5}{6} r^{2}-\frac{2}{3}=\frac{3}{4}$$

$$\frac{\pm \sqrt{170}}{10}$$

Algebra

Chapter 0

Reviewing the Basics

Section 2

Solving Equations of the Form $a x^{2}-b=0$

Equations and Inequalities

Campbell University

Oregon State University

Harvey Mudd College

Lectures

02:00

Find the unknown.$$\fr…

Find the unknown.$$(2 …

00:52

Find the unknown.$$r^{…

01:50

Evaluate each expression f…

00:29

Explain how to evaluate an…

00:20

Compute, as indicated.…

01:52

01:23

00:41

Calculate.$$5\left[3-8…

01:26

so we're asked to solve for R in this problem. That's the unknown. Um, and there's a lot of different options that you can do to solve this. I don't want to just give you just I guess I'm just going to show you one way, because I want to keep this video so much short. The easiest thing to do is get the, uh, common multiple, Um, least common multiple for the denominators. So as you're looking at the number 63 and four, um, the least common multiple for that I believe would be 12, right? All those are divisible by 12 so I can multiply everyone in these terms because I'm multi on both sides of the equation by 12. I guess it's technically what I'm doing. Distribute that in there, distribute this in here until, uh, this is acceptable. We can do that because 12, 2 by sixes two times five or give me 10 r squared and then 12 by by three is four times to give me eight 12. Divided by four is three times through. Give me nine. So then, from here I can I can get r squared by itself. The first step would be to add eight over. So I have 10 R squared on the left side. Nine plus eight is 17, and then I can get R squared by itself by dividing both sides by 10. So R squared will equal 17/10. Um, and then, to solve a square problem, you just square root both sides. Now here's the thing. Some teachers won't let you just leave your answer as, uh, plus or minus the square root of 17/10, because it's not a simplest radical form, so I just show you a quick trip trip. To do this is multiply top and bottom by the same thing. So I'm just doing Route 10 because it's easier. Um, and what you'll get then is plus or minus. Well, you can multiply the radicals together. So route 17 times through 10 and the route 170 and route 10 times. Route 10 is just 10. If you're confused by that, what you really have is the square root of 100 the denominator and scored a 100 is 10. Um, now, this is not simplify a ble. You can't simplify that anymore. You could try to simplify the numerator, but 17 is prime in 10 breaks down to two and five, so there's no pairs to bring in front. This is your best answer. The square root of 170 all over 10. The positive negative version of that that's our

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