Solve For $g$.$\sqrt{9g} = \sqrt{-9 + 10g}$g =$

Introduction

In this article, we will delve into the world of algebra and focus on solving a specific equation involving the variable g. The given equation is $\sqrt{9g} = \sqrt{-9 + 10g}$. Our goal is to isolate the variable g and find its value. We will break down the solution into manageable steps, making it easier to understand and follow along.

Step 1: Square Both Sides of the Equation

The first step in solving this equation is to square both sides of the equation. This will help us eliminate the square roots and make it easier to work with the equation.

$\left(\sqrt{9g}\right)^2 = \left(\sqrt{-9 + 10g}\right)^2$

Squaring both sides of the equation gives us:

$9g = -9 + 10g$

Step 2: Simplify the Equation

Now that we have squared both sides of the equation, we can simplify it by combining like terms.

$9g = -9 + 10g$

Subtracting 9g from both sides of the equation gives us:

$0 = -9 + g$

Step 3: Isolate the Variable g

Our goal is to isolate the variable g, so we need to get rid of the constant term on the right-hand side of the equation.

$0 = -9 + g$

Adding 9 to both sides of the equation gives us:

$9 = g$

Conclusion

In this article, we have solved the equation $\sqrt{9g} = \sqrt{-9 + 10g}$ for the variable g. By squaring both sides of the equation and simplifying, we were able to isolate the variable g and find its value. The final answer is:

$g = 9$

Final Answer

$$

Introduction

In this article, we will delve into the world of algebra and focus on solving a specific equation involving the variable g. The given equation is $\sqrt{9g} = \sqrt{-9 + 10g}$. Our goal is to isolate the variable g and find its value. We will break down the solution into manageable steps, making it easier to understand and follow along.

Step 1: Square Both Sides of the Equation

The first step in solving this equation is to square both sides of the equation. This will help us eliminate the square roots and make it easier to work with the equation.

$\left(\sqrt{9g}\right)^2 = \left(\sqrt{-9 + 10g}\right)^2$

Squaring both sides of the equation gives us:

$9g = -9 + 10g$

Step 2: Simplify the Equation

Now that we have squared both sides of the equation, we can simplify it by combining like terms.

$9g = -9 + 10g$

Subtracting 9g from both sides of the equation gives us:

$0 = -9 + g$

Step 3: Isolate the Variable g

Our goal is to isolate the variable g, so we need to get rid of the constant term on the right-hand side of the equation.

$0 = -9 + g$

Adding 9 to both sides of the equation gives us:

$9 = g$

Conclusion

In this article, we have solved the equation $\sqrt{9g} = \sqrt{-9 + 10g}$ for the variable g. By squaring both sides of the equation and simplifying, we were able to isolate the variable g and find its value. The final answer is:

$g = 9$

Final Answer

The final answer is $\boxed{9}$.

Q: What is the given equation?

A: The given equation is $\sqrt{9g} = \sqrt{-9 + 10g}$.

Q: What is the goal of solving this equation?

A: The goal of solving this equation is to isolate the variable g and find its value.

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

A: The first step in solving this equation is to square both sides of the equation.

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

A: We square both sides of the equation to eliminate the square roots and make it easier to work with the equation.

Q: What is the final answer to the equation?

A: The final answer to the equation is $g = 9$.

Q: How do we isolate the variable g?

A: We isolate the variable g by getting rid of the constant term on the right-hand side of the equation.

Q: What is the importance of isolating the variable g?

A: Isolating the variable g is important because it allows us to find its value and understand the relationship between the variables in the equation.

Q: Can you provide an example of a real-world application of solving for g?

A: Yes, solving for g can be applied to various real-world scenarios, such as calculating the acceleration of an object or determining the value of a variable in a scientific experiment.

Q: What are some common mistakes to avoid when solving for g?

A: Some common mistakes to avoid when solving for g include:

• Not squaring both sides of the equation
• Not simplifying the equation
• Not isolating the variable g
• Not checking the solution for validity

Q: How can I practice solving for g?

A: You can practice solving for g by working on similar equations and problems. You can also use online resources, such as math websites and apps, to practice and improve your skills.