General > General Technical Chat
I can't solve a simple equation. Help please.
<< < (3/3)
SilverSolder:

--- Quote from: Terry Bites on February 05, 2021, 01:47:05 pm ---Just because its my birthday.... (Attachment Link)
MS mathematics- Handy, free, works... https://math.microsoft.com/en

--- End quote ---

This is actually rather good - a no BS application!  Remember those?

To download the last standalone desktop application:

https://www.microsoft.com/en-us/download/details.aspx?id=15702

You can say "No" to installing the ancient version of DirectX, with no ill effects
vad:
Another vote for Maxima / wxMaxima.
rstofer:
You can plug the equation in at www.symbolab.com, get both solutions.

IanB:

--- Quote from: intabits on February 02, 2021, 07:40:12 pm ---Thanks to all who replied.

Yes, I did manage to get to
ax^2 + axb - b = 0       

So I knew it was a quadratic, though I didn't think to divide by a to get
x^2 + bx - b/a = 0      

My usual method was to then try to factorize it into something like
(x - 1/a)(x + b) = 0       (incorrect)
and then find the roots by seeing when each of the two factors becomes zero.

I know that's not always possible, and that the quadratic formula was a method to handle that situation.
But although we were taught it, I can't ever recall actually using it!
So I didn't, hoping there was some simpler method.
Though that is (now) obviously the method to use.
--- End quote ---

Here is the way to do it if you can't remember the quadratic formula.

Start with the reduced quadratic:

x² + bx - b/a = 0

Now construct a similar equation that is easier to solve:

(x + b/2)² = 0

If we multiply this out, we get:

x² + bx + b²/4 = 0

We can make this similar equation the same as the equation we want like this:

x² + bx + b²/4 − b²/4 − b/a = x² + bx − b/a = 0

But now we are in a position to solve the original equation:

(x² + bx + b²/4) − b²/4 − b/a = (x + b/2)² − b²/4 − b/a = 0

We have:

(x + b/2)² − b²/4 − b/a = 0
(x + b/2)² = b²/4 + b/a
x + b/2 = ± √(b²/4 + b/a)

Therefore:

x = − b/2 ± √(b^2/4 + b/a)

This is the same answer as already presented above, and this method (called "completing the square") is how the quadratic formula is originally obtained.


intabits:
Thanks for the explanation. "completing the square" is a familiar term, but I'd long forgotten what it involved.
Navigation
Message Index
Previous page
There was an error while thanking
Thanking...

Go to full version
Powered by SMFPacks Advanced Attachments Uploader Mod