00:00The absolute value of x plus 0.77 (repeating character) multiplied by x minus 3 equals 0.55 (since it's a repeating decimal).
00:09The question asks us to find the product of the possible values of x.
00:13Now, regarding repeating numbers, we know that when we say 0.7, if 7 is a repeating decimal, what is it?
00:20That part at the top where the revolutions are going goes up to step 0.777, folks, that's the end result.
00:27That's what it's trying to express, cyclical, as the name suggests.
00:30In this case, we can write the repeating decimal of 0.7 as 7 divided by 9, in short, folks.
00:35We saw it in the numbers, right guys?
00:37We used to write it as: whole number minus non-repeating part divided by as many 9s as there are repeating parts and as many 0s as there are non-repeating parts.
00:42So now, with a 0.5 5 revolution cycle, it goes all the way down to 0.555.
00:51So what happens then, folks? We write the same thing here again, with a 0.5 RPM speed.
00:56We say 9 because there's one rollover.
00:58Having written this, friends, I want to get straight to the point.
01:05This is a question in this process.
01:07What was X plus 0.7?
01:097 out of 9.
01:12Minus 3.
01:14That one has a repeating decimal of 0.5, let's say that one is 5/9.
01:20Okay guys, when this happens, there are two solutions.
01:24What was the first one?
01:25You wanted to write something like this.
01:279 times x 9 x 7 more is 16 x divided by 9 minus 3 equals.
01:385 divided by 9, right guys?
01:42Let's think about it this way.
01:43The first one is either this is 5/9 plus 5/9.
01:49Or, friends, this is 16 x minus 3.
01:53This will be number 9, folks.
01:575 out of 9.
01:58Let's not prolong this scene.
01:59What is this place, friends?
02:01It is minus 5 divided by 9.
02:02Isn't that right?
02:03Ultimately, this is equal to 5 divided by 9 in absolute value.
02:06It's either 5/9 or minus 5/9 inside, so it comes out as 5/9 outside.
02:10Okay, let's do this, guys.
02:11Let's call it a one.
02:13Let's be the first to do it.
02:1416 x divided by 9 minus 3, which equals 5 divided by 9 plus 5 divided by 9.
02:20I'll do it right away.
02:21I'm throwing -3 over here, guys.
02:23Those who know, put them on one side; those who don't know, put them on the other.
02:2516x divided by 9 is equal to 3 plus 5 divided by 9.
02:30That's also equivalent to rational estimations.
02:339 times 3 is 27, how much is 5?
02:3632 divided by 9.
02:38So, 16x divided by 9 is equal to 32 divided by 9.
02:43Here, we can simplify things from both sides, friends.
02:461 16 simplifies to 2.
02:48The 9s simplify to 1:1.
02:50When we divide by 9.
02:51X equals 2.
02:53We found this from here.
02:54Now let's get to this point.
02:55To the second one.
02:57And in the second one, friends.
02:5916 x divided by 9 minus 3 of us.
03:03And we based it on minus 5 divided by 9, right?
03:05Yes.
03:06If we move -3 from here to the other side, what happens, guys?
03:09It counts as +3.
03:1116 x divided by 9.
03:13That's equal to 3 minus 5 divided by 9.
03:16That is equal to 9 times 3 = 27.
03:18Subtracting 5 from 22 is 9.
03:21So, 16 times x divided by 9 equals 22 divided by 9.
03:27The 9s are simplified.
03:28What do we do with this place, guys?
03:29Simplify by dividing by 2 to get 8.
03:31Simplify by dividing by 2 to get 11.
03:32X equals 11 divided by 8.
03:36So, friends, what were we being asked?
03:39Of course, the question was about the product of these two values.
03:42Let's call this x1.
03:43Let's call it x2.
03:44x1 times x2.
03:46That's equal to 2 times 11 divided by 8.
03:48That equals 2 and 8, which simplify.
03:511, 4.
03:52So what does that equal, friends?
03:54We find our answer as 11 divided by 4.
03:56We will find the answer.
03:57We say we've found the answer.
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