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Find the unknown.$$\frac{1}{5}(3 x-5)^{2}+\frac{2}{3}=2$$

$$\frac{15 \pm 2 \sqrt{15}}{9}$$

Algebra

Chapter 0

Reviewing the Basics

Section 2

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

Equations and Inequalities

Oregon State University

McMaster University

Baylor University

University of Michigan - Ann Arbor

Lectures

02:16

Find the unknown.$$(3 …

01:57

01:24

Find the unknown.$$(x+…

01:45

Find the unknown.$$(5 …

01:00

Find the unknown.$$5 x…

01:41

Solve.$$\frac{2}{5 x+5…

02:47

01:01

Evaluate.$\frac{2\left…

So we're looking at solving for X, and I like to get rid of fractions. So that's what I'm gonna do that's too. So what I'm looking for is the least common multiple of the denominator, which in this case five times three is 15. So that's at least common number of that. Both five and three go into so I can distribute that 15 into this problem, and I can recognize that 15 divided by five is three. I'm gonna leave this three x minus Bible wound because it's part of that term and then 15 times to 30 divided by three is 10 is equal to over here two times 15. It's 30. So now I can try to get my three x minus five squared term alone by subtracting 10 over. I don't cancel that out and divide both sides by three. So on the left side, I just have that three x minus five squared. And on the right side I get 20 divided by three. So now what I can do is I can undo the square by square, rooting both sides. Just make sure that you understand that when you square root you do get to answers. A positive and a negative. Um, Now, most math teachers do not like the route in the denominator. So what you'll do is rationalize the denominator by multiplying top and bottom by route three. Okay, so on the left side, you have this three X minus five. And on the right side, you stood the plus or minus. Um, and the Delano route three times, right. Three is route nine, which is three. Alright, right here. And over here, you get route 60 and if you break down Route 60 email, write this off to the side. That's the same thing as the square root of four times. The square to 15 square to four is too. So to route 15 now, my next step would be to get this negative five to the other side, so I would add five over. But as I'm looking at the answer, they like to leave. The denominator is the same. Um, So what they did, I believe, is they changed. Fix that. And seven adding five over. They rewrote as 15 3rd. It's is equal, different table for five. So then you're denominators are the same, and we can put them together 15 plus minus 2 15 all over three. And instead of dividing by three, I think a lot of people do that. I'm going to multiply by one third. And the reason I like to show that is then you can see will multiply. Fraction used to multiply the denominators together So three times three is nine. So our best answer would look like this. 15 plus or minus two. Route 15 all over. No.

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