Solve for X | Math Problem | Paul's Question

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Discussion Overview

The discussion revolves around a math problem posed by a user named Paul, who seeks assistance in solving for the variable x in the equation derived from an expression involving two variables. The scope includes algebraic manipulation and problem-solving techniques.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Paul initially presents an expression involving two variables and requests help in finding x.
  • Some participants point out that the original expression is not an equation and ask for clarification on what it equals.
  • Paul later clarifies that the expression is equal to zero, thus forming an equation to solve.
  • One participant reformulates the equation using variables a, b, c, d, and e for clarity and provides a step-by-step algebraic manipulation to isolate x.
  • The participant presents two cases based on the signs of the terms involved, leading to different expressions for x depending on the assumptions made about the signs.
  • There is an acknowledgment that if there are errors in the provided steps, other participants may point them out.

Areas of Agreement / Disagreement

Participants generally agree on the need to clarify the original expression and its transformation into an equation. However, there is no consensus on the correctness of the algebraic manipulations presented, as no corrections or confirmations have been made yet.

Contextual Notes

The discussion involves assumptions about the signs of the variables, which may affect the validity of the derived expressions for x. The dependence on the values of n and the constants a, b, c, d, and e is also noted but not resolved.

Jones1812
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Hi, my name is Paul and I'm new to this forum. I'm having a math problem that I'm unable to find a solution for it at all, i have tried many solutions but unable to find the x
(0.149/(18 - 0.1x - 0.05n)^2) - (44.5/x^2)
The task is to find the variable x
Thanks a lot, your help will mean a lot to me.
 
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what you have posted is an expression in two variables, not an equation

does $\dfrac{0.149}{(18 - 0.1x - 0.05n)^2} - \dfrac{44.5}{x^2} = \text{ anything ?}$
 
skeeter said:
what you have posted is an expression in two variables, not an equation

does $\dfrac{0.149}{(18 - 0.1x - 0.05n)^2} - \dfrac{44.5}{x^2} = \text{ anything ?}$
I'm so so so sorry for the mistake, the above expression is equal to 0.
 
$\dfrac{0.149}{(18 - 0.1x - 0.05n)^2} - \dfrac{44.5}{x^2} = 0$

replacing the constants with $a,b,c,d, e$ to make the algebra easier to follow ...

$\dfrac{a}{(b - cx - dn)^2} - \dfrac{e}{x^2} = 0$

$\dfrac{a}{(b - cx - dn)^2} = \dfrac{e}{x^2}$

$\dfrac{\sqrt{a}}{|b-cx-dn|} = \dfrac{\sqrt{e}}{|x|}$

assuming both $(b-cx-dn)$ and $x$ are same-signed (both positive or both negative) ...

$\dfrac{\sqrt{a}}{b-cx-dn} = \dfrac{\sqrt{e}}{x}$

$x\sqrt{\dfrac{a}{e}} = b-cx-dn$

$x\sqrt{\dfrac{a}{e}}+cx = b-dn$

$x\left(\sqrt{\dfrac{a}{e}} + c \right) = b-dn$

$x = \dfrac{b-dn}{\sqrt{\dfrac{a}{e}} + c}$

assuming $(b-cx-dn)$ and $x$ are different signed (one positive, the other negative) ...

$\dfrac{\sqrt{a}}{dn+cx-b} = \dfrac{\sqrt{e}}{x}$

$x\sqrt{\dfrac{a}{e}} = dn+cx-b$

$x\sqrt{\dfrac{a}{e}}-cx = dn-b$

$x\left(\sqrt{\dfrac{a}{e}} - c \right) = dn-b$

$x = \dfrac{dn-b}{\sqrt{\dfrac{a}{e}} - c}$Hope this works for you ... if I erred somewhere, I'm sure someone will jump on this thread and point out the mistake.
 

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