Any mathematicians out there?

[barryjbutler]

Can anyone take me through the resoultion of the equation
24/x = 10-x

By observation there are two answers, 4 and 6, but the process eludes me.

[daisya]

Can you find the answer here?

http://www.math10.com...lgebra/equations.html

[roslyn251254]

24/x = 10-x
multiply both sides by x ..... 24 = x(10-x)
24 = 10x -xsquared
xsquared -10x =24 =o
(x-4)(x-6)=0
so x= 4 or x=6

[plautus]

Multiply throughout by x

24 = 10x -x²

Rearrange: x² - 10 = 0

Factorise: (x -6) (x - 4) =0

x = 6 or x = 4

[plautus]

Sorry, should read:

Multiply throughout by x

24 = 10x -x²

Rearrange: x² - 10 + 24 = 0

Factorise: (x -6) (x - 4) =0

x = 6 or x = 4

[roslyn251254]

plautus - which keys for typing x squared?

[Fibonacci]

as the rhs is divided by x
multiply every part of the equation by x giving
24 = 10x - x^2
rearrange to give 24 - 10x + x^2 =0
or x^2 - 10x + 24 = 0
this can be factorised
(x - 6)(x - 4) = 0
so x -6 = 0 and hence x = 6
or x - 4 = and hence x = 4

[Prudie]

This is a quadratic equation which will have 2 roots(answers). First get rid of the x on the bottom by multiplying each term by x. this gives:
24=10x-x^2
Then bring all the terms to the left side of the equal sign so it looks more familiar(remembering that anything you move must change sign). This will give;
x^2-10x+24=0
Now factorise into 2 brackets (hope you get that bit?)
So (x-6)(x-4)=0
So either x-6=0 so x is6 or x-4=0 so x is 4

[Prudie]

gawd I type too slow!

[barryjbutler]

Many thanks. I'd got as far as the factorise position and lost my way.

[plautus]

Type x then with number lock on hold down ALT key and type 253 on the number pad (not the top row)

[Prudie]

No way on a laptop then plautus?

[roslyn251254]

Thanks plautus - useful info!

[gen2]

Follow these steps
a) lose the denominator by multiplying both sides by 'x'
b) Take everything on the right-hand side and subtract it from both sides

You will be left with a quadratic function of 'x' equal to 0
c) factorise that function of 'x' into the form (ax +- b)(cx +- d)
If two expressions multiplied together = zero, then one of them must be 0
so either (ax +- b) = 0
or (cx +- d) = 0
d) Solve each of those for the two possible answers.

If you cannot factorise the quadratic, then use the formula for solving quadratics:

x = (-b +- SQR(b^2 -4ac)) / 2a
(I hope I have remembered that correctly from over 40 years ago)

[plautus]

Have you not got a number pad on your keyboard? If not try this. I don't know if it will work but it does for me:

Turn on num lock. On my small keyboard the letters M J K L U I O generate the numbers 1 - 6, 7 to 9 being on the top row. So hold down ALT and type KIL instead. let me know if it works or not.

[plautus]

That should read 0 - 6.

[boxtops]

Does that work on laptops, plautus?

[plautus]

If you have a number pad yes. I have a laptop and a small plug-in keypad as I wrecked the one on my laptop. Give it a try.

[Prudie]

Hi plautus there is no number keys apart from the top row so there's no numlock either. when I pressed Alt and any key it didn't do anything. I think I've seen on here that you can paste indices into a post from Word but I've never got round to trying.

[beso]

Well done gen2.

I remember it too but it has only been a bit over thirty years for me.

[plautus]

The keyboard I am using at the moment has no number pad but has a num lock key on the top right. I used that plus the letters I gave to generate ².

This might be useful to some people who want to generate diacritics and other symbols:
http://www.irongeek.c...combos-and-chart.html