Solving the Equation x/25 196/x: A Step-by-Step Guide

Looking for a detailed walkthrough on solving the equation x/25 196/x? Here, we will break down the process with clear steps and explanations. This guide is ideal for students in math, as well as anyone seeking to enhance their algebraic skills.

Introduction to the Equation

Consider the equation: x/25 196/x. This is a classic example of a proportion or a rational equation where the variables are in the numerators and denominators. Such equations often appear in algebra and math problem-solving contexts. Let's explore how to solve it step by step.

Solving x/25 196/x

The goal is to find the value of x. Here's a detailed breakdown:

Step 1: Cross Multiplication

To solve the equation x/25 196/x, the first approach is to cross multiply. This means multiplying both sides of the equation by the denominators. In this case, multiply both sides by 25x:

x * 25x / 25  196x / x * 25x

Simplifying both sides, we get:

x^2  25 * 196

Step 2: Simplification and Square Root

The next step is to simplify the right-hand side of the equation:

x^2  25 * 196  4900

To find x, take the square root of both sides:

x  ±√4900

Breaking down the square root:

x  ±√(5^2 * 7^2 * 2^2 * 7^2)  ±(5 * 7 * 2 * 7)  ±70

Conclusion

The solutions to the equation x/25 196/x are x 70 and x -70. In many practical applications, we often consider positive solutions unless specified otherwise.

Practice Questions and Additional Resources

Now that you've seen the solution process, it's time to practice! Try solving similar equations with different values. If you’re looking for more resources, consider checking out:

Online math problem solvers Algebra textbooks and workbooks YouTube tutorials on solving algebraic equations Interactive math websites and apps

Remember, the key to mastering algebra is consistent practice and a good understanding of the underlying principles.