Solve Quadratic Equations for x: Mechanics Notes & Error Check

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Discussion Overview

The discussion revolves around solving a quadratic equation related to mechanics, with participants examining discrepancies between calculated roots and those noted in the original problem. The scope includes mathematical reasoning and error checking in calculations.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant reports that their calculations yield a positive root of 2.12, while their notes suggest it should be 3.
  • Another participant challenges the correctness of both proposed roots, stating that neither 3 nor 2.12 are roots of the equation as presented.
  • A different participant suggests that 3 could be a correct root if the left-hand side of the equation is modified to include 144x² instead of 144 + x².
  • One participant points out that substituting x=10 leads to an incorrect equation, indicating a mistake in the formulation of the problem.
  • Another participant confirms that the equation is valid and clarifies that solving it involves finding values of x that satisfy the equation.
  • A later reply mentions reducing the original equation to a specific quadratic form, yielding roots of approximately 4.604 and 7.984.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the roots and the formulation of the equation, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

There are indications of missing assumptions regarding the original equation's structure, and the discussion reflects uncertainty about the correct formulation and simplification steps.

RStars
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Hey,

I was going through some mechanics notes and came across this quadratic equation to solve for x. In my notes it is supposed to equal 3 however I do not get that result. I am not sure if I am simplifying it wrong or what. I am ending up with 2.12 for the positive value. Please let me know if you get 3 or 2.12 so that I know if the error is in my calculations or in my notes.

http://img707.imageshack.us/img707/338/codecogseqno.gif

Thanks in advanced.
 
Last edited by a moderator:
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RStars said:
Hey,

I was going through some mechanics notes and came across this quadratic equation to solve for x. In my notes it is supposed to equal 3 however I do not get that result. I am not sure if I am simplifying it wrong or what. I am ending up with 2.12 for the positive value. Please let me know if you get 3 or 2.12 so that I know if the error is in my calculations or in my notes.

http://img707.imageshack.us/img707/338/codecogseqno.gif

Thanks in advanced.



It must be some mistake in your notes: if you put x=3 in the given eq., one gets that the LHS is not an integer

whereas the RHS is...

DonAntonio
 
Last edited by a moderator:
Neither 3 nor 2.12 are roots of the equation as you wrote it.
 
3 is correct if the LHS is amended to contain 144x2 rather than 144 + x2.
 
um... I haven't done this in a while so forgive me for being simple... but that's not an equation.

if you put x=10 you end up with the equation 122=900, which isn't true.

There's been some kind of mistake.
 
evilbrent said:
um... I haven't done this in a while so forgive me for being simple... but that's not an equation.

if you put x=10 you end up with the equation 122=900, which isn't true.

There's been some kind of mistake.



No, that is too an equation. To solve it means to find out the numerical values of x that when substituted in the equation give

a true equality. What you've shown above is that the numerical value x = 10 is not (one of the) a solution(s) of the equation.

DonAntonio
 
oh, ok, yes. Sorry engineering maths was a decade ago for me. It's amazing how quickly the knowledge vanishes.

I reduced the original equation down to 0=-71.5x^2+900x-2628 and got 0=(x-4.604)*(x-7.984)
 

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