How to solve for x in this equation

  • Thread starter frankivalli
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In summary, the conversation discusses the difficulty of solving for "x" in the equation provided, which is related to finding the height of a liquid in a cylindrical tank. The speaker mentions that it may not be possible to solve the equation analytically and suggests using numerical methods. They also mention the concept of transcendental equations and suggest using a numerical or graphical solution.
  • #1
frankivalli
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How to solve for "x" in this equation

Thanks in advance:

here is my equation:

Area = [itex]\pi[/itex]r[itex]^{2}[/itex] - r[itex]^{2}[/itex](arcos((r-x)/r))+(r-x))*[itex]\sqrt{2*r*x-x^{2}}[/itex]
 
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  • #2
frankivalli said:
Thanks in advance:

here is my equation:

Area = [itex]\pi[/itex]r[itex]^{2}[/itex] - r[itex]^{2}[/itex](arcos((r-x)/r))+(r-x))*[itex]\sqrt{2*r*x-x^{2}}[/itex]
Is this related to the question you asked in another thread about the height of a liquid in a horizontal, cylindrical tank?

If so, I don't think you can solve the equation above analytically for x. The best you can do is solve it numerically using some approximation technique.
 

1. How do I know which method to use to solve for x in an equation?

There are several methods for solving equations, including substitution, elimination, and graphing. The best method to use depends on the type of equation and the given information. You can determine the most appropriate method by carefully examining the equation and identifying any patterns or relationships.

2. Can I solve for x in an equation with more than one variable?

Yes, it is possible to solve for x in an equation with multiple variables. However, you will need to have enough information to eliminate all other variables and isolate x. This may require using multiple equations or methods.

3. What do I do if there are fractions or decimals in the equation?

If there are fractions or decimals in the equation, you can eliminate them by multiplying both sides of the equation by the common denominator. This will result in a new equation with whole numbers that can be solved using the appropriate method.

4. Can I solve for x if the equation is not in standard form?

Yes, you can still solve for x if the equation is not in standard form. You may need to rearrange the terms and use properties of equality to get the equation into a more manageable form. Once the equation is simplified, you can proceed with solving for x.

5. Is there a shortcut or trick to solving equations quickly?

While there are some strategies and shortcuts that can make solving equations faster, there is no one-size-fits-all approach. It is important to carefully analyze the equation and use the appropriate methods to solve for x. With practice and understanding of mathematical concepts, you can become quicker at solving equations.

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