Melody

Now to answer you real question.

Where did I go wrong!

I expect you know that   

$$\\3a+4a=(3+4)a\\\\
and\\\
xa+6a = (x+6)a\\\\
$say a was not $a$ but just some expression.$\\\\
3(x+2)+4(x+2\\=3 \; lots\; of\; (x+2)+4 \; lots\; of\; (x+2)\\= (3+4)\; lots\; of\; (x+2) \\= 7(x+2)\\\\
x(x+2)+6(x+2)\\=x \; lots\; of\; (x+2)+6 \; lots\; of\; (x+2)\\= (x+6)\; lots\; of\; (x+2) \\= (x+6)(x+2)\\\\$$

Now, this is what you wrote:

$$\\x(x-2)+6(x-1)\\\\(x+6)(2x-3)\\$$

You cannot do this because you have x lots of (x-2)  and 6 lots of (x-1)  

The brackets are not the same - they are unlike terms - you cannot add them like you have done :/

Hi Purpe,

Alan is right. Only expressions with rational roots can be done the 'factoring in pairs' way.

Yours is 

$$\\2(x^2+4x-6)=0\\\\
x^2+4x-6=0\\\\$$

Now you have to look for 2 numbers that multiply to 1*-6=-6

Since they multiply to a negative, one is pos and the other is neg

They have to add to +4

So the 'bigger' (absolute value) one is positive

There are no 2 rational numbers that meet this requirement so you cannot do it this way!

There are a number of methods that you can use.

Alan has shown you one of them.

I would just solve it using the quadratic formula :))

I want to try pepper and butter popcorn too MG.  It sounds pretty good :))

Would it be reasonable for me to do it like this?

A population of fruit flies starts with 6 flies. On Day 4, the population has grown to 94 flies. Write an exponential growth function to model the growth of the fly population.

$$\\P=6e^{k(t-1)}\\\\
94=6e^{3k}\\\\
15.\dot6 = e^{3k} \\\\
ln(15.\bar6 )= ln(e^{3k}) \\\\
ln(15.\bar6 )= 3k \\\\
k=ln(15.\bar6 )/3 \\\\
k\approx 0.91718\\\\
so\\\\
P=6e^{0.91718(t-1)}\\\\$$

Is that ok?

Lets see

I will type  5^x=25 into the input box

Output:

$${{\mathtt{5}}}^{{\mathtt{x}}} = {\mathtt{25}} \Rightarrow {\mathtt{x}} = {\frac{{ln}{\left({\mathtt{25}}\right)}}{{ln}{\left({\mathtt{5}}\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{2}}$$

There you go - that worked   :))

infinity

But this is a concept - not a number :)

I think you should join up and post a pic because I do not know what you are talking about.  Sorry :/

7x-15+1x=5+2x

There's a start :)

Melody44

Australia has states NOT provinces :))

I don't care if a is rational.  I am not rational so why should a be.  That would not be fair. :))

Should b or not b be rational.  Only c would know I suppose :)

Thanks Alan. :)