Solve The Equation: 10 M − 1 − 2 M + 7 = 0 \sqrt{10m - 1} - \sqrt{2m + 7} = 0 10 M − 1 ​ − 2 M + 7 ​ = 0

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Introduction

Solving equations involving square roots can be a challenging task in mathematics. In this article, we will focus on solving the equation $\sqrt{10m - 1} - \sqrt{2m + 7} = 0$. This equation involves two square roots, and our goal is to find the value of $m$ that satisfies this equation. We will use algebraic techniques to simplify the equation and solve for $m$.

Step 1: Simplifying the Equation

To simplify the equation, we can start by isolating one of the square roots. Let's isolate the first square root:

$\sqrt{10m - 1} = \sqrt{2m + 7}$

Step 2: Squaring Both Sides

To eliminate the square roots, we can square both sides of the equation:

$(\sqrt{10m - 1})^2 = (\sqrt{2m + 7})^2$

This simplifies to:

$10m - 1 = 2m + 7$

Step 3: Solving for $m$

Now we can solve for $m$ by isolating the variable on one side of the equation:

$10m - 2m = 7 + 1$

This simplifies to:

$8m = 8$

Step 4: Dividing Both Sides

To find the value of $m$, we can divide both sides of the equation by 8:

$m = \frac{8}{8}$

This simplifies to:

$m = 1$

Conclusion

In this article, we solved the equation $\sqrt{10m - 1} - \sqrt{2m + 7} = 0$ using algebraic techniques. We started by isolating one of the square roots, then squared both sides of the equation to eliminate the square roots. Finally, we solved for $m$ by isolating the variable on one side of the equation. The value of $m$ that satisfies this equation is $m = 1$.

Example Use Case

This equation can be used in a variety of real-world applications, such as:

• Physics: The equation can be used to model the motion of an object under the influence of gravity.
• Engineering: The equation can be used to design and optimize systems, such as bridges and buildings.
• Computer Science: The equation can be used to develop algorithms and data structures for solving problems involving square roots.

Tips and Tricks

When solving equations involving square roots, it's often helpful to:

• Isolate one of the square roots: This can make it easier to eliminate the square roots and solve for the variable.
• Square both sides: This can help to eliminate the square roots and simplify the equation.
• Check your work: Make sure to check your solution by plugging it back into the original equation.

Common Mistakes

When solving equations involving square roots, it's easy to make mistakes, such as:

• Forgetting to square both sides: This can lead to an incorrect solution.
• Not checking your work: This can lead to an incorrect solution.
• Not using the correct algebraic techniques: This can lead to an incorrect solution.

Conclusion

Solving equations involving square roots can be a challenging task, but with the right techniques and strategies, it's possible to find the solution. In this article, we solved the equation $\sqrt{10m - 1} - \sqrt{2m + 7} = 0$ using algebraic techniques. We started by isolating one of the square roots, then squared both sides of the equation to eliminate the square roots. Finally, we solved for $m$ by isolating the variable on one side of the equation. The value of $m$ that satisfies this equation is $m = 1$.

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Introduction

In our previous article, we solved the equation $\sqrt{10m - 1} - \sqrt{2m + 7} = 0$ using algebraic techniques. In this article, we will answer some common questions that readers may have about solving this equation.

Q: What is the first step in solving the equation?

A: The first step in solving the equation is to isolate one of the square roots. In this case, we can isolate the first square root by moving the second square root to the other side of the equation.

Q: Why do we need to square both sides of the equation?

A: We need to square both sides of the equation to eliminate the square roots. This is because the square root of a number is equal to the number raised to the power of 1/2. By squaring both sides of the equation, we can get rid of the square roots and simplify the equation.

Q: How do we know which side of the equation to square?

A: We can square either side of the equation, but it's often easier to square the side with the variable (in this case, $m$). This is because squaring the side with the variable will give us a simpler equation to work with.

Q: What if the equation has more than two square roots?

A: If the equation has more than two square roots, we can still use the same techniques to solve it. We can isolate one of the square roots, square both sides of the equation, and then repeat the process until we have eliminated all of the square roots.

Q: Can we use other algebraic techniques to solve the equation?

A: Yes, we can use other algebraic techniques to solve the equation. For example, we can use the quadratic formula to solve the equation, or we can use substitution to simplify the equation.

Q: What if we get a negative value for $m$?

A: If we get a negative value for $m$, it means that the equation has no real solutions. This is because the square root of a negative number is not a real number.

Q: Can we use this equation in real-world applications?

A: Yes, we can use this equation in real-world applications. For example, we can use it to model the motion of an object under the influence of gravity, or we can use it to design and optimize systems, such as bridges and buildings.

Q: What are some common mistakes to avoid when solving this equation?

A: Some common mistakes to avoid when solving this equation include:

• Forgetting to square both sides of the equation
• Not checking your work
• Not using the correct algebraic techniques

Q: How can we check our work?

A: We can check our work by plugging our solution back into the original equation. If the equation is true, then our solution is correct.

Conclusion

Solving the equation $\sqrt{10m - 1} - \sqrt{2m + 7} = 0$ can be a challenging task, but with the right techniques and strategies, it's possible to find the solution. In this article, we answered some common questions that readers may have about solving this equation. We hope that this article has been helpful in understanding how to solve this equation.

Additional Resources

If you're interested in learning more about solving equations involving square roots, we recommend checking out the following resources:

• Algebra textbooks: There are many algebra textbooks that cover solving equations involving square roots.
• Online resources: There are many online resources, such as Khan Academy and Mathway, that provide step-by-step instructions on how to solve equations involving square roots.
• Practice problems: Practice problems are a great way to reinforce your understanding of solving equations involving square roots.

Final Thoughts

Solving equations involving square roots can be a challenging task, but with the right techniques and strategies, it's possible to find the solution. We hope that this article has been helpful in understanding how to solve the equation $\sqrt{10m - 1} - \sqrt{2m + 7} = 0$. If you have any further questions or need additional help, please don't hesitate to ask.