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I need to turn the equation L=12/x + x into a quadratic forumla to solve. i have been given the answers of 0.619m 0r 19.38m if L = 20m

what iv go so far

0= 12/x + x -20 but i dont know how to turn 12/x to a x^2 value

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2 Answers 2

Multiply the equation by $x$ and you'll get the polynomial you want.

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$$ \begin{align} L &= \dfrac{12}{x} + x \\ Lx &= 12 + x^2 & (\text{multiplying both sides by x}) \\ x^2 + 12 - Lx &= 0 \\ \\ \text{For L = 20,} \\ x^2 - 20x + 12 &= 0 \\ \\ \text{Solving using the quadratic formula} \\ x = 0.619 \text{ or } x = 19.380 & \text{as required} \end{align} $$

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Oops, sorry just realized this question is 8 months old! –  mathguy80 Jul 24 '11 at 15:41
    
How did you happen to come across such an old question? It's funny. –  mixedmath Jul 24 '11 at 19:21
    
Hah! It was the top item in the related list on the sidebar while I was asking a new question. –  mathguy80 Jul 25 '11 at 3:20
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