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

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Discussion Overview

The discussion revolves around solving the equation \(\frac{x^2}{18}-\frac{x}{9}=1\) using the method of completing the square. Participants are exploring the steps involved in manipulating the equation to reach a solution.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant expresses confusion about how to start solving the equation.
  • Another participant suggests multiplying through by the lowest common denominator (18) to eliminate the fractions, leading to the equation \(x^2 - 2x = 18\).
  • A later reply indicates uncertainty about how to proceed after reaching the simplified equation.
  • Another participant proposes taking half of the coefficient of the linear term and squaring it, suggesting this as a step to complete the square.

Areas of Agreement / Disagreement

Participants generally express uncertainty and confusion, with no consensus on how to proceed with the solution.

Contextual Notes

Participants have not fully resolved the steps needed to complete the square, and there are missing assumptions regarding the manipulation of the equation.

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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