2nd degree equation difficulty

In summary: I see - I was thinking of the UK keyboards...In summary, the conversation discussed how to solve an equation without external aids, using only mental arithmetic and without a calculator or formula sheet. The equation given was 9(x-2)= 3x(x-2), and it was suggested to rewrite it as (9 - 3x)(x - 2) = 0 to simplify the solution process. The conversation also addressed the use of absolute value notation and how to type equations using LaTeX. Ultimately, it was concluded that the easiest way to solve the equation was to recognize the common factor and simplify from there.
  • #1
301
15

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)
 
Physics news on Phys.org
  • #2
late347 said:

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.
late347 said:

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.
late347 said:
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.
 
  • #3
late347 said:

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".
 
  • #4
Mark44 said:
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.
 
  • #5
late347 said:
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!
 
  • #6
Ray Vickson said:
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
 
  • #7
late347 said:
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).
 
  • #8
Mark44 said:
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.
 
  • #9
epenguin said:
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 (\).
 

1. What is a 2nd degree equation?

A 2nd degree equation, also known as a quadratic equation, is an algebraic equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. It is called a 2nd degree equation because the highest exponent in the equation is 2.

2. How do you solve a 2nd degree equation?

To solve a 2nd degree equation, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. Alternatively, you can factor the equation or complete the square to find the solutions.

3. What are the different types of solutions for a 2nd degree equation?

A 2nd degree equation can have two real solutions, one real solution, or two complex solutions. Real solutions are values of x that make the equation true, while complex solutions involve the use of imaginary numbers.

4. How do you graph a 2nd degree equation?

To graph a 2nd degree equation, you can plot points on a coordinate plane, use the axis of symmetry and vertex, or use transformations from the basic parabola y = x². The graph of a 2nd degree equation is always a parabola.

5. Where are 2nd degree equations used in real life?

2nd degree equations are used in many fields of science, engineering, and finance, as they can model a wide range of physical phenomena and behaviors. They can be used to predict the trajectory of a projectile, the shape of a satellite's orbit, or the maximum profit for a business.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
1
Views
858
  • Precalculus Mathematics Homework Help
Replies
8
Views
476
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
2
Replies
39
Views
2K
  • Precalculus Mathematics Homework Help
Replies
8
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
13
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
  • Precalculus Mathematics Homework Help
Replies
10
Views
2K
Back
Top