2nd degree equation difficulty

[late347]

Homework Statement

[/B]

Solve without external aids. You may use memorized 2nd degree equation formula.

9(x-2)= 3x(x-2)

Homework Equations

3. The Attempt at a Solution [/B]

Use memorized 2nd degree equation formula

9x-18= 3x^2 -6x ]]] + 18
9x= 3x^2 -6x +18 ]]] -9x
0 = 3x²-15x + 18
After some tiresome calculation with pen-and-paper

I reached conclusion that

x is either

(15+3) /6 = 3

or

(15-3) / 6 = 2

x either 2 or 3

I wonder if there is an easier way to solve the equation with only mental arithmetic of course... (no calculator no formula sheet)

 

[Mark44]

Homework Statement

[/B]

Solve without external aids. You may use memorized 2nd degree equation formula.

9(x-2)= 3x(x-2)

It's much simpler to rewrite this equation as (9 - 3x)(x - 2) = 0, after which the solutions can be found very easily.

Homework Equations

3. The Attempt at a Solution [/B]

Use memorized 2nd degree equation formula

9x-18= 3x^2 -6x ]]] + 18
9x= 3x^2 -6x +18 ]]] -9x

The ]]] business above took me a while to figure out what you're doing.

0 = 3x²-15x + 18
After some tiresome calculation with pen-and-paper

I reached conclusion that

x is either

(15+3) /6 = 3

or

(15-3) / 6 = 2

x either 2 or 3

I wonder if there is an easier way to solve the equation with only mental arithmetic of course... (no calculator no formula sheet)

See above.

 

[Ray Vickson]

Homework Statement

[/B]

Solve without external aids. You may use memorized 2nd degree equation formula.

9(x-2)= 3x(x-2)

Homework Equations

3. The Attempt at a Solution [/B]

Use memorized 2nd degree equation formula

9x-18= 3x^2 -6x ]]] + 18
9x= 3x^2 -6x +18 ]]] -9x
0 = 3x²-15x + 18
After some tiresome calculation with pen-and-paper

I reached conclusion that

x is either

(15+3) /6 = 3

or

(15-3) / 6 = 2

x either 2 or 3

I wonder if there is an easier way to solve the equation with only mental arithmetic of course... (no calculator no formula sheet)

Mark44 has shown you the easier way.

You should realize, however, that the easier way does not always work in every problem, and sometimes you need to use the "memorized 2nd degree formula".

 

[late347]

It's much simpler to rewrite this equation as (9 - 3x)(x - 2) = 0, after which the solutions can be found very easily.
The ]]] business above took me a while to figure out what you're doing.
See above.

we were taught to use twin-absolute value signs at the end of the equation (with nothing inside of the signs) to signify that both sides of the equation are being operated upon

I coould not find that absolute value notation so I simply used the ]] to stand in its own stead.

|| + 18 means that 18 is added to both sides.

Some people simply switch terms of the equation and flip the sign, but it helps to avoid getting confused, when you do it by operating on both sides of the equation with some arithmetic operation.

 

[Ray Vickson]

we were taught to use twin-absolute value signs at the end of the equation (with nothing inside of the signs) to signify that both sides of the equation are being operated upon

I coould not find that absolute value notation so I simply used the ]] to stand in its own stead.

|| + 18 means that 18 is added to both sides.

Some people simply switch terms of the equation and flip the sign, but it helps to avoid getting confused, when you do it by operating on both sides of the equation with some arithmetic operation.

You say you could not find the absolute value notation, but now you have used it!

 

[late347]

You say you could not find the absolute value notation, but now you have used it!

I copy-pasted it from wikipedia article

I cannot find absolutevalue easily in the insert symbol list of mathematical notation.

furthermore how is it possible to write the code for things like cubic roots and n-th root of X for instance

 

[Ray Vickson]

I copy-pasted it from wikipedia article

I cannot find absolutevalue easily in the insert symbol list of mathematical notation.

furthermore how is it possible to write the code for things like cubic roots and n-th root of X for instance

Every computer keyboard I have ever seen has an absolute value key somewhere. Also, when you post an article in this Forum there is a gray band at the top of the input panel, and if you click the Σ sign, you will get a large variety of mathematical symbols you can copy and paste into your submission. It does not seem to have an absolute value sign, but as I said, your keyboard will have one.As for things like $\sqrt[n]{x^2+2 \theta \log \sin x}$, etc., just use LaTeX, which is available on this Forum. (You can right-click on the formula I just wrote to see how it is typed in LaTeX.

You can certainly enter quite easily anything you will ever need using LaTeX; in particular, there is a double absolute value sign built in, like this: $a \| b$. However, to type it you need to use your keyboard's "|" key (by typing \| in the LaTeX expression).

 

[epenguin]

It's much simpler to rewrite this equation as (9 - 3x)(x - 2) = 0, after which the solutions can be found very easily.
The ]]] business above took me a while to figure out what you're doing.
See above.

You don't even need to do that IMO.

You have the same factor on left and right – if it is 0 then the equation is satisfied so then x = 2.

If it is not 0 then you can 'cancel it out', i.e. divide the whole equation by it and then you get 9 = 3x ...

The | on most keyboards is the very first symbol, the top left capital key.

 

[Mark44]

The | on most keyboards is the very first symbol, the top left capital key.

Not on QWERTY keyboards sold in the US. On those keyboards, it's on the right, above the slash (\).