Solve Completing Square Problem: ((x2)/18)-(x/9)=1

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SUMMARY

The discussion revolves around solving the equation \(\frac{x^2}{18} - \frac{x}{9} = 1\) by completing the square. The initial step involves multiplying through by 18 to eliminate the denominators, resulting in the equation \(x^2 - 2x = 18\). Participants suggest taking half of the linear coefficient (-2), squaring it, and adding it to both sides to complete the square. This method is essential for transforming the quadratic equation into a solvable format.

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wellyn
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help I am stumped on this ((x2)/18)-(x/9)=1(Headbang)(Headbang)(Headbang)(Headbang)
 
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Re: competing the square

wellyn said:
help I am stumped on this ((x2)/18)-(x/9)=1(Headbang)(Headbang)(Headbang)(Headbang)

We are given:

$$\frac{x^2}{18}-\frac{x}{9}=1$$

I think I would first multiply through by the lowest common denominator to get rid of the denominators. So, multiplying through by 18, we get:

$$x^2-2x=18$$

Can you proceed?
 
Re: competing the square

no sorry I am stumped
 
Re: competing the square

wellyn said:
no sorry I am stumped

You want to take half the coefficient of the linear term (the term with $x$ as a factor) and square it, and add this to both sides. What do you get?
 

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