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Find the unknown.$$\frac{3}{2}(3 y-2)^{2}-18=0$$

$$\frac{2 \pm 2 \sqrt{3}}{3}$$

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

McMaster University

Harvey Mudd College

Lectures

01:59

Find the unknown.$$(2 …

02:26

Find the unknown.$$\fr…

00:24

Find the unknown.$$y^{…

00:36

Find the unknown.$$2 y…

01:58

Find the unknown.$$(y-…

01:30

Solve the equation. $$…

02:19

Find $d y$$$2 y^{3 / 2…

01:24

Solve. $(y-3)^{2}=0$

02:10

Solve.$$(3 y+2)^{2}+(3…

01:05

Solve.$$3 y^{2}+8 y+2=…

01:31

Solve. $3 y^{2}-18 y=-…

we're solving for why, in this problem, we have three halves times three y minus two squared quantity squared minus 18 is equal to zero. So the whole goal would be to get this, um, squared piece by itself, which is not too bad. We can start by adding 18 over. So, on the right side, we have zero plus 18 is 18. Instead of rewriting all of this, I'm just going to talk about to undo this. Multiplied by a fraction. You don't do that by multiplying both sides by the reciprocal there are simple of three halves is two thirds. You can see that those two pieces will cancel out. So on the left side, Yeah, you're just left with three minus two squared and on the right side. When you simplify Now, I would just do, um, 18 times two. I would actually do 18. Divided by 36 times two is 12. That's how I would do that math in my head. So then, from there we can simplify the square. We can solve it by square rooting. So those pieces cancel out and we can break down 12 with four and three and four breaks down is two times two. In other words, you can say that Route 12 is the same thing as Route four times Route three and the square to four is to Route three. Just don't forget about plus or minus like I almost did. And on the left side you just have that three y minus two, and we're pretty much really close to being done. We just have to get why by itself, and you can quickly do that by adding two to the right side. So we always write the whole part in front of the irrational part. So this two goes in front of the plus or minus two Route three all over because we in order to solve a multiplication problem, you divide both sides by three, and this is a perfect answer for why we're done ready to move on

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