# Solve for X | Math Problem | Paul's Question

• MHB
• Jones1812
In summary, the conversation involved a person named Paul seeking help with a math problem involving an expression in two variables. After realizing the mistake, the expression was equal to 0, and the task was to find the value of the variable x. Through algebraic manipulation, two possible solutions were provided based on the assumption of both variables being either same-signed or different-signed.
Jones1812
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.

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.

## 1. What does "solving for X" mean?

When solving for X, you are trying to find the value of the variable X that makes the given equation or problem true.

## 2. How do I solve for X?

To solve for X, you need to isolate the variable on one side of the equation by using algebraic operations such as addition, subtraction, multiplication, and division. Remember to perform the same operation on both sides of the equation to maintain balance.

## 3. What are the steps to solve a math problem with X?

The steps to solve a math problem with X will vary depending on the type of problem and equation given. However, some general steps include identifying the variable, combining like terms, isolating the variable, and checking your answer by plugging it back into the original equation.

## 4. Can you give an example of solving for X?

Sure, for example, if the equation is 2X + 3 = 9, you would first subtract 3 from both sides to isolate the variable, giving you 2X = 6. Then, you would divide both sides by 2 to get the value of X, which in this case is 3.

## 5. Why is solving for X important?

Solving for X is important because it allows us to find the unknown value in an equation or problem. This is useful in many real-life situations, such as calculating the cost of an item on sale, determining the time it takes to travel a certain distance, or finding the missing angle in a geometry problem.

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