Question

solutions to 6x^2=18x

Answer 1

First, you need to set it to zero. Then find the factors.

Answer 2

Hope it helps

Answer 3

@50_cent copy and paste is not correct!
You copied and pasted from the website: http://www.geteasysolution.com/6x%5E2-18x=0

Answer 4

@50_cent thats not even the same equation :(

Answer 5

@e.mccormick i don't understand. How??

Answer 6

If you look at what I said, it is the set it to 0 part.

Answer 7

\(6x^2=18x\implies 6x^2-18x=18x-18x\implies 6x^2-18x=0\)

Answer 8

1. Subtract 18x from both sides
2. Factor out the common factor 6x
3. Set each factor equal to 0
4. Solve each equation
5. Write your answers.

Answer 9

Hehe. We are all saying the same thing. OK.. so, now, do you get the first step?

Answer 10

lols ikr. Is there more steps? :0 my teacher told me the answer was x=0 x=3 and i just want to find out how she got that xD..and No i dont get it lol

Answer 11

Solve for x over the real numbers:
6 x^2 = 18 x
Move everything to the left hand side.
Subtract 18 x from both sides:
6 x^2-18 x = 0
Factor the left hand side.
Factor x and constant terms from the left hand side:
6 (x-3) x = 0
Divide both sides by a constant to simplify the equation.
Divide both sides by 6:
(x-3) x = 0
Solve each term in the product separately.
Split into two equations:
x-3 = 0 or x = 0
Look at the first equation: Solve for x.
Add 3 to both sides:
Answer: |
| x = 3 or x = 0

Answer 12

@freethinker ahh :D thank you!!

Answer 13

\[6 x^2-18 x = 0\]
\[x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]
\[x = \frac{ -(-18) \pm \sqrt{(-18)^2 - 4(6)(0)} }{ 2(6) }\]
\[x = \frac{ 18 \pm \sqrt{324 - 0} }{ 12 }\]
\[x = \frac{ 18 \pm \sqrt{324} }{ 12 }\]
\[x = \frac{ 18 \pm 18 }{ 12 }\]
\[x = \frac{ 18 + 18 }{ 12 }\]
\[x = \frac{ 36}{ 12 }\]
\[x = 3\]
\[x = \frac{ 18 - 18 }{ 12 }\]
\[x = \frac{ 0 }{ 12 }\]
\[x = 0\]

Answer 14

that too
to complete the square

Answer 15

And there it is with the quadratic formula. Wheee.

Yah. What freethinker did is where it all goes from where I was starting. The point here is learning about factors.

Know how you sometimes factor a number? Like \(14=7\cdot 2\) or \(125=5\cdot 5\cdot 5\). These principals carry over into algebra. The factors of \(6 x^2-18 x \) are the things that would multiply together to make it. Factoring is un-multiplying, which is not the same as dividing.

Answer 16

Algerbra is hard .-. ...But that made me understand more @e.mccormick Thanks! :3

Answer 17

lol im the only one without a medal :( haha

Answer 18

Mertsj didn't get one.... but Mertsj has more than enough medals... =P

Answer 19

lol yeah he does ;)

Answer 20

Solve for x over the real numbers:
6 x^2 = 18 x
Move everything to the left hand side.
Subtract 18 x from both sides:
6 x^2-18 x = 0
Write the quadratic equation in standard form.
Divide both sides by 6:
x^2-3 x = 0
Take one half of the coefficient of x and square it, then add it to both sides.
Add 9/4 to both sides:
x^2-3 x+9/4 = 9/4
Factor the left hand side.
Write the left hand side as a square:
(x-3/2)^2 = 9/4
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x-3/2 = 3/2 or x-3/2 = -3/2
Look at the first equation: Solve for x.
Add 3/2 to both sides:
x = 3 or x-3/2 = -3/2
Look at the second equation: Solve for x.
Add 3/2 to both sides:
Answer: |
| x = 3 or x = 0

Answer 21

woah woah woah dude. you cant just change how you solve it @freethinker now im confused as hell xD

Answer 22

nawww it's another way of solving it called completing the square.

Answer 23

6 (x-3) x = 0
Divide both sides by a constant to simplify the equation
--------
in here when u divide by 6..what else is getting divided by 6?

Answer 24

oooh havnt heard of it xD

Answer 25

both sides of the eQUATION.

Answer 26

.-. oh

Answer 27

6 (x-3) x = 0
-------- --
6 6

6 ON the left-hand side (LHS) cancels out leaving you with (x-3)

0 divided by 6 is 0

Answer 28

Lesson #2 about math... there is more than one way to skin a factoring problem. You just saw three valid solutions. Here is a fourth, it is a graphical one. Where do the lines meet? What are the x values at those points?

Answer 29

hmm. Interesting.

Answer 30

Find a method that works for you. Get used to it. But remember that you may be required to use other methods in the future. By keeping up on old skills and developing new ones, you can tackle pretty much any problem as the come along.

Also, many degrees these days require you take calculus. The vast majority of a calculus class is not calculus, it is trig and algebra and geometry and even arithmetic. So if you are better at these basic skills, you will do better in calculus.

Answer 31

The best method was the first you gave me . :) ill keep this in mind! i appreciate it thanks.

Answer 32

Exactly, for something this simple, the easy factor is there. For something more complex, there is the big gun of the quadratic formula. If it is for a circle or hyperbola solution, you MUST use completing the square. All are tools, all have a job, use the right tool and it is easy... wrong tool and it can be a lot more work to get the same answer!

Answer 33

true true. i checked on google and it gave me something totally different!

Answer 34

What did you find there?

Answer 35

the same answer 50 cent gave me.

Answer 36

@frann what math course are you taking? Also what math knowledge do you have? For example, general math, pre-algebra, algebra 1, algebra 2, ... etc.

Answer 37

That is important cuz with that we know till what to show you. Like for example, you might not heard of completing the square since you probably have not gotten there in math.

Answer 38

Algerbra 1 . But struggling ;-;

Answer 39

There are many good math references out there. I have used many, but when it comes to algebra I do have a favorite.

http://www.purplemath.com/modules/index.htm

If you match up the name of what you are doing in your class to the topics there, you can usually find a good description. Many are not too long. However, there are complex topics where they take several pages to go over and do multiple examples. I find they have more information than most textbooks I have seen coupled with a practical way of presentation.

That way you can learn the techniques, not the answers. If you know the techniques, the answers are there for the picking!

Answer 40

hmm okaii.

Answer 41

:) thank yew haha. Some websites out there never really help including my actual
math teacher

Answer 42

yah, I looked at that http://www.geteasysolution.com/6x%5E2-18x=0 thing and it is technically right.... but it is presented poorly. You have to know what it means to know how it got there. If you knew what it meant, you would not need the information. So it is worthless!

Answer 43

@e.mccormick i never said it was wrong, i didn't even take a look at it; in depth. I just said that the user copied and pasted the answer from there lol :P

Answer 44

The best one ive used was yourteacher.com but after the free trial you had to pay. so i was bummed out :/ It was the ONLY one that i understood

Answer 45

@some_someone Hehe. I am not saying you said it was wrong. I know you meant it was wrong of him to just do that. I am saying that without an explanation, that web site is worthless, which is pretty much what you were pointing out too.

Answer 46

lol yep :)

Answer 47

lol how random @Luis_Rivera

Answer 48

@frann

One other problem with math teachers is that many forget to tell you that you are in a language class. Mathematics is a language. It has all these terms that mean very specific things in math. If you just keep teaching math like it is counting things on one hand, with no explanation that you are now entering a new language, how will you ever expect these odd bits of grammar and "strange" terms?

Let me give you an example. This is actually related to algebra 1, but I bet you would not know a lot of what it says.

It is given that \(\{a, b, x, x_1, x_2\}\in \mathbb{R}\) and \(x_1\ne x_2\). If \(x=\{x_1,x_2\}\) for \(ax=b\) then:
\(ax_1=b;\, ax_2=b \)
\[b=b\\
\implies ax_1= ax_2 \\
\implies x_1= x_2 \forall x_1, x_2\]\(\because x_1\ne x_2,\; ax=b\) must only have one solution.
Q.E.D.

Answer 49

*o* ooh.

Answer 50

hey @Luis_Rivera :D

Answer 51

how will you ever expect these odd bits of grammar and "strange" terms? ... oops... to make sense was supposed to be in there somewhere.

Answer 52

its ok ! :D i understood it

Answer 53

What that bottom part means is that \(3x=9\) has only one answer, \(x=3\). But it is what they call a proof. They use things like \(\in\) which is "in" or "is a member of" and \(\implies\) implies.

Answer 54

its like using symbols :o and meaning and stuff

Answer 55

Like ;P and ;-) and so on. Exactly. It is a language. That language has rules, like what "solutions to \(6x^2=18x\)" means and what it implies about how to get there. If you were sad, you would not send out ;P, you would send ;-; or :( out. What the message means implies things. What the formula or question given menas is the same thing.

Answer 56

menas.... doh. Ignore the lysdexia. Means.

Answer 57

hahaha menas. well i suppose i can use math as a lanuguage now .But i wont be so good on it.

Answer 58

Well, lets come full circle. I am just talking about a concept so you can help understand why math is almost alien at times.

That equation, \(6x^2=18x\) can be read as "where does the curve six ex squared equal or intersect with the line eighteen ex?"

Answer 59

The answer to it stated that way is the picture I linked where they cross. It is just one reading of the language. But understanding the intent leads to all the possible methods of getting that solution.

Answer 60

ooooh thats how you got the points. Could be represented as (0,3)

Answer 61

Yes, and when you know a language, you know how you can say the same things diferent ways.

Hello \(\implies\) Hi \(\implies\) What's up! \(\implies\) Yo

\(6x^2=18x\implies 6x^2-18x=0\)

Answer 62

ooh i see. i have one more problem, if you can help me answer it?

Answer 63

Sure. I am just talking conseptual stuff now because you seemed to need to connect with the math a bit more.

Answer 64

yess hehe :) .
A company builds computers. It costs 6,700 to build 10 computers and 12,00 to build 20 computers. which equation models the cost c(x) as a linear function of the number of computers build?

Answer 65

12,00 or 12,000?


The language is the one used by Mathematicians... a strange breed the came out of Philosophers. We are not sure how... probably genetic drift or survival instinct. =P But once Mathematicians started breeding, they infested every country and became deeply vested in all the sciences. So knowing their language is a necessary part of dealing with a large chunk of our world.

If you want a truly bizarre language, learn Philosophy itself. There they have had questions documented as having been asked 3000 years ago, and they are still trying to find an answer!

Answer 66

1200. :) and philosophy itself is confusing enough.

Answer 67

12,200...OOPS!

Answer 68

ah. K.

Now, what are the important numbers and words in that problem. Tell me which ones you see and I'll tell you which ones I see.

Answer 69

I see 6,700 and 12,200

Answer 70

I see:
costs 6,700 to build 10
costs 12,200 to build 20
cost c(x) as a linear function of the number of computers build

Answer 71

What do you think "a linear function" means?

Answer 72

When the slope is equal? I think :E

Answer 73

Not bad. Sort of. What do you think "a \(\huge \mathrm{line}\)ar function" means? (big hint)

Answer 74

when the line of the slope is straight?

Answer 75

Yes, some of math is this basic and uncreative. A curve has a slope that changes, and many other things. A line, well, is a line.... it is straight and goes forever, so we deal with little segments we can see and understand. In this case, they want a function that makes a line.

Answer 76

So, if we are looking for the equation of a line, and have these things:
costs 6,700 to build 10
costs 12,200 to build 20

And we are told that function is to find the cost c(x), what does that make those numbers?

Answer 77

it makes it linear?

Answer 78

Line = Linear But I am taling more like:

Answer 79

So which is the x and which is the y? And do you know how to find the slope of a line from two points?

Answer 80

yes : \[\frac{ y _{2}-y _{1} }{ x _{2} -x _{1}}\]

Answer 81

OK. So, what is the \((x_1,y_1)\) and what is the \((x_2,y_2)\)?

Answer 82

The Ordinate is ordinary Y or Results. The Abscissa is the x. But those terms confuse people, so we will stick with Y and X axis.

We have c(x) on the y axis and x on the... wait for it... x axis. (not surprising it is there.) That makes the x,y points into what?

Answer 83

(6,700 , 12,200) (10 , 20) ?

Answer 84

That is two outputs together and teo inputs together... not quite right.