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

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To solve the equation (x^2)/18 - (x/9) = 1, the first step is to eliminate the denominators by multiplying through by 18, resulting in the equation x^2 - 2x = 18. Next, to complete the square, half the coefficient of the linear term (-2) is squared and added to both sides. This results in a new equation that can be solved for x. The discussion highlights the process of completing the square as a method to simplify and solve the quadratic equation effectively.
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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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