# Quick question on High-School equations.

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So I had my exam-like test today and after doing some parts of a task I suddenly came to a stop: What do I do if this happens? I can't get that number to appear in small just above and to the right of a number, so I do this instead: something(2) = something*something 3x(2)-11x = 24 I had a little problem with that... Can you guys tell me what to do in such situations? Thank you!

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Well, you transfer the 24 to the other side and create this

3x^2-11x-24=0

Then you use Cubic equation to solve it:

(-b+-root(b^2-4*a*c))/2a

And you should get 2 answers of this equation.

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Ill explain..

What you see there is a quadratic equation, and it should have been handled fully at your school, and they should teach you how to solve it using
A: Formula
B: Factorisation
C: Completion of the Square

First lets get it in the STANDARD quadratic equation form which is "ax^2 + bx + c = 0"

THEN PLEASE NOTE That quadratics always have 2 answers, and sometimes you get a repeated answer in which case both answers are just the same, however not all of the answers are REAL NUMBERS and so the others we will ignore :-)

3x(2)-11x = 24 ----> 3x^2 - 11x + 24 = 0
// Now not every single quadratic can be solved by factorisation so the formula as samsonite gave you is
-----------------------
________
-b + _/ b*b - 4ac
x = ---------------------------------
2a
________
-b - _/ b*b - 4ac
x = ---------------------------------
2a

As you see the sign infront of the square root just changed which is why the formala will be written with a +- sign on top of each other

....
Now Completion of the Square is a variation on the vactorisation it involves an advanced method of factorisation (*which is how the formula was originally worked out*)

if we have the quadratic in this shape
ax*x + bx+c = 0
then we re-arrane to get
x*x + bx/a = -c/a
And now we add (bx/a)*(bx/a) to both sides so we get
x*x + bx/a + (b/2a)^2 = -c/a + (b/2a)^2
Now we can factorise the left side like this
(x + b/2a)^2 = -c/a + b^2/4a^2
which gives
______________ _________________
_/(x + b/2a)^2 =_/ -c/a + b^2/4a^2
which becomes
________________
x =_/ -c/a + b^2/4a^2 - b/2a

// Consider that which is under the Square root
-c/a + b^2/4a^2 can become

(b^2-4ac)
------------
4a^2

// Which leaves
----------------
x =_/ (B^2 - 4ac)
---------- - b/2a
4a^2

and finaly we can take 4a^2 up one by sqr rooting it

----------------
x =_/ (B^2 - 4ac) * 2a - b/2a

Common de-numerators

----------------
x = -b + _/ (B^2 - 4ac)
-------------------
2a

And logic says that a square root can be either + or - and so thats why it really is

----------------
x = -b +-_/ (B^2 - 4ac)
-------------------
2a

Hope thats not 2 much theory for one night

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Quote:
 Original post by dawidjoubert3x(2)-11x = 24 ----> 3x^2 - 11x + 24 = 0

It's actually 3x^2 - 11x - 24 = 0

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Quote:
 Original post by SamsoniteI can't get that number to appear in small just above and to the right of a number, so I do this instead:

Just for reference [smile], use plain html: < sup>superscript here</sup > -> superscript here

Looks like your other question has been comprehensively answered. [smile]

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To summarize on what has already been said:

An equation which is of the form ax2 + bx + c = 0 where a, b and c are constants drawn from an algebraic field (typically the complex numbers) is called a quadratic equation because it is a second-order polynomial. Note that "of the form" is a precise mathematical term meaning, in this case, that your equation does not need to be in that form initially, only that it can be put into that form. Your equation, therefore, is of that form.

For solving quadratic equations you use the quadratic formula:

An alternative form is

You may also rest assured that because quadratics are second-order polynomials that the fundamental theorem of algebra guarantees two solutions in the field of complex numbers (which contains the real numbers as a subfield).

[Edited by - nilkn on November 28, 2005 8:02:57 PM]

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nilkn i see you gave an alternative formula.. COOL.. i didnt know theres another shape to it.

Is there more alternatives?

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This won't help you anymore. Well, it might help with memorization...just a bit.

We learned quadratic formula with a song -- "X equals opposite b, plus or minus the square root of (b squared minus four-a-c), all over two-a."

...Ok, so it's not much of a song, and it doesn't have much rhythm, but say it enough times and you won't forget it.

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Quote:
 Original post by Boku SanThis won't help you anymore. Well, it might help with memorization...just a bit.We learned quadratic formula with a song -- "X equals opposite b, plus or minus the square root of (b squared minus four-a-c), all over two-a."...Ok, so it's not much of a song, and it doesn't have much rhythm, but say it enough times and you won't forget it.

Lol, hahaha thats the cutest thing i have ever heard!!

No thanks i am well adept at memorizing it. But thanks

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Quote:
 Original post by dawidjoubertnilkn i see you gave an alternative formula.. COOL.. i didnt know theres another shape to it.Is there more alternatives?

Heh, actually I wasn't even aware there was an alternative form. I got the images of the formula from MathWorld, and they had an alternative form listed, so I thought I might as well post it. [smile]

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