Is This the Right Way to Solve a Quadratic Equation?

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Discussion Overview

The discussion revolves around the method for solving a quadratic equation, specifically the equation 2(x - 5)² = 32. Participants explore the steps taken to simplify and solve the equation, including dividing both sides by 2 and taking the square root.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether dividing both sides of the equation by 2 is acceptable.
  • Another participant confirms that the method used is correct and that all steps are valid.
  • A third participant suggests an alternative approach by rearranging the equation as a difference of squares.
  • This alternative method leads to the same roots, x = 1 and x = 9, but through a different algebraic manipulation.

Areas of Agreement / Disagreement

Participants generally agree on the validity of the method used to solve the quadratic equation, though an alternative approach is also presented without any disagreement on the correctness of the original method.

Contextual Notes

The discussion does not address any potential limitations or assumptions in the methods presented, nor does it explore the implications of using different algebraic techniques.

Casio1
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Hi everyone(Wink)

I have an equation which looks like quadratic to me.

2(x - 5)2 = 32

Can I divide both sides by 2?

(x - 5)2 = 16

Can I take the square root?

x - 5 = + or - 4

if x = 5 plus 4 = 9

if x = 5 - 4 = 1

Therefore my roots would be;

x = 9 or x = 1

Is this method acceptable and the correct way to find the values of x. I know it works out OK but am wondering about the way I have done it?

Thanks
 
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Hi Casio!

(Yes) Well done. That's exactly how you should do this problem every step of the way.
 
Yes, that is a perfectly valid procedure. All of your steps are correct. (Nod)
 
After dividing by 2, we may also arrange as the difference of squares:

(x - 5)2 - 42 = 0

((x - 5) + 4)((x - 5) - 4) = 0

(x - 1)(x - 9) = 0

x = 1, 9
 

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