Hi,

I'm trying to work out how a question was solved from an example in a book.

x(squared)

------------------- = 6.25

6 - 5x + x(squared)

goes to...

5.25x(squared) - 31.25x + 37.5 = 0

I don't understand how this was done.

any ideas?

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- Dec 2nd 2008, 09:17 AMLarianneTurning a fraction into a quadratic
Hi,

I'm trying to work out how a question was solved from an example in a book.

x(squared)

------------------- = 6.25

6 - 5x + x(squared)

goes to...

5.25x(squared) - 31.25x + 37.5 = 0

I don't understand how this was done.

any ideas? - Dec 2nd 2008, 10:03 AMnzmathman
They have cross multiplied to get the answer.

$\displaystyle \frac{x^2}{6 - 5x + x^2} = 6.25$

$\displaystyle \Rightarrow x^2 = 6.25(6 - 5x + x^2) $ (cross multiply)

$\displaystyle \Rightarrow x^2 = 37.5 - 31.25x + 6.25x^2 $ (expanding)

$\displaystyle \Rightarrow 5.25x^2 - 31.25x + 37.5 = 0 $ (collect terms on one side)