How do I solve for R in this equation?

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In summary, the conversation is about solving an equation involving square roots and finding the domain of solutions. The person is struggling to remember the steps and methods to solve the equation and is seeking help. They mention their initial thought of squaring both sides but are unsure of how it would help. The other person suggests moving the single R to the other side before squaring both sides and reminds them to be careful with specifying the domain of solutions.
  • #1
zgozvrm
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Homework Statement



This is not homework; I'm working on a problem of my own...


I can't seem to remember how to solve equations like this (I'm trying to solve for R):

[tex]R - \sqrt{R^2 - X^2} \le B - \sqrt{B^2 - \left( \frac{BX}{A} \right) ^2}[/tex]

Homework Equations



My initial thought was to square both sides, but I don't see how that would help.

The Attempt at a Solution



I don't really know where to start.
 
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  • #2
You need to get rid of the square root expression containing R^2.
Move your single R over to the other side, and THEN square both sides.

You'll need to be careful when specifying the domain of solutions.
 
  • #3
Yeah, thanks. I just drew a blank for some reason!
 

FAQ: How do I solve for R in this equation?

How do you solve for R in a mathematical equation?

The process for solving for R will depend on the specific equation you are working with. Generally, you will need to isolate the variable R on one side of the equation by using algebraic operations such as addition, subtraction, multiplication, or division. Once R is isolated, you can solve for its value by plugging in the known values for the other variables in the equation.

Can you provide an example of solving for R in a real-life scenario?

Solving for R is a common task in various fields, such as physics, engineering, and finance. For example, if you know the force and mass of an object and want to calculate its acceleration, you can use the equation F = ma and solve for a by dividing both sides by m. The resulting equation, a = F/m, allows you to determine the acceleration (R) of the object.

What are some common mistakes to avoid when solving for R?

One common mistake is forgetting to perform the same operation on both sides of the equation. For example, if you divide one side of the equation by a number, you must also divide the other side by the same number to maintain balance. Another mistake is incorrectly applying the order of operations, which can lead to an incorrect solution.

Are there any shortcuts or tricks for solving for R?

There are various strategies and techniques that can make solving for R easier, such as factoring, using the distributive property, or applying the quadratic formula. It is essential to practice and familiarize yourself with these methods to become more efficient at solving equations.

Can solving for R be done using a calculator?

Yes, solving for R can be done using a calculator, especially for more complex equations. However, it is still crucial to understand the underlying principles and steps involved in solving equations manually, as calculators can sometimes provide incorrect solutions if the input is not entered correctly.

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