Solve The Equation:$-5+\sqrt{x+4}=2$

$$

Introduction

Solving equations involving square roots can be a challenging task, especially when the variable is inside the square root. In this article, we will focus on solving the equation $-5+\sqrt{x+4}=2$ step by step. We will use algebraic manipulations and properties of square roots to isolate the variable and find its value.

Understanding the Equation

The given equation is $-5+\sqrt{x+4}=2$. Our goal is to solve for the variable $x$. To do this, we need to isolate the square root term and then square both sides of the equation to eliminate the square root.

Isolating the Square Root Term

To isolate the square root term, we can start by adding $5$ to both sides of the equation. This will give us:

$$\sqrt{x+4}=2+5$$

Simplifying the right-hand side, we get:

$$\sqrt{x+4}=7$$

Squaring Both Sides

Now that we have isolated the square root term, we can square both sides of the equation to eliminate the square root. Squaring both sides gives us:

$$(\sqrt{x+4})^2=(7)^2$$

Using the property of square roots that $(\sqrt{a})^2=a$, we can simplify the left-hand side to get:

$$x+4=49$$

Solving for $x$

Now that we have simplified the equation, we can solve for $x$ by subtracting $4$ from both sides:

$$x=49-4$$

Simplifying the right-hand side, we get:

$$x=45$$

Verifying the Solution

To verify our solution, we can plug $x=45$ back into the original equation and check if it is true. Substituting $x=45$ into the original equation, we get:

$$-5+\sqrt{45+4}=2$$

Simplifying the expression inside the square root, we get:

$$-5+\sqrt{49}=2$$

Using the property of square roots that $\sqrt{a^2}=|a|$, we can simplify the right-hand side to get:

$$-5+7=2$$

Simplifying the left-hand side, we get:

$$2=2$$

Since the equation is true, we can conclude that $x=45$ is indeed the solution to the equation.

Conclusion

In this article, we solved the equation $-5+\sqrt{x+4}=2$ step by step. We isolated the square root term, squared both sides of the equation, and solved for $x$. We also verified our solution by plugging it back into the original equation. The final answer is $x=45$.

Frequently Asked Questions

• Q: What is the first step in solving the equation $-5+\sqrt{x+4}=2$? A: The first step is to isolate the square root term by adding $5$ to both sides of the equation.
• Q: What is the property of square roots that we used to simplify the left-hand side of the equation? A: The property of square roots that we used is $(\sqrt{a})^2=a$.
• Q: How do we verify the solution to the equation? A: We verify the solution by plugging it back into the original equation and checking if it is true.

Additional Resources

• For more information on solving equations involving square roots, see the article "Solving Equations with Square Roots".
• For more practice problems on solving equations involving square roots, see the worksheet "Solving Equations with Square Roots Practice".

References

• [1] "Solving Equations with Square Roots" by Math Open Reference
• [2] "Solving Equations with Square Roots Practice" by Mathway

Related Articles

• Solving Equations with Absolute Values
• Solving Equations with Fractions
• Solving Equations with Exponents
  

$$

Introduction

In our previous article, we solved the equation $-5+\sqrt{x+4}=2$ step by step. We isolated the square root term, squared both sides of the equation, and solved for $x$. We also verified our solution by plugging it back into the original equation. In this article, we will answer some frequently asked questions related to solving the equation $-5+\sqrt{x+4}=2$.

Q&A

Q: What is the first step in solving the equation $-5+\sqrt{x+4}=2$?

A: The first step is to isolate the square root term by adding $5$ to both sides of the equation. This will give us $\sqrt{x+4}=7$.

Q: What is the property of square roots that we used to simplify the left-hand side of the equation?

A: The property of square roots that we used is $(\sqrt{a})^2=a$. This property allows us to simplify the left-hand side of the equation by removing the square root.

Q: How do we verify the solution to the equation?

A: We verify the solution by plugging it back into the original equation and checking if it is true. In this case, we plugged $x=45$ back into the original equation and checked if it is true.

Q: What if the equation has a negative number inside the square root?

A: If the equation has a negative number inside the square root, we cannot take the square root of the number. In this case, we need to use a different method to solve the equation.

Q: Can we use the same method to solve equations with absolute values?

A: No, we cannot use the same method to solve equations with absolute values. Equations with absolute values require a different method to solve.

Q: What is the final answer to the equation $-5+\sqrt{x+4}=2$?

A: The final answer to the equation $-5+\sqrt{x+4}=2$ is $x=45$.

Q: Can we use a calculator to solve the equation $-5+\sqrt{x+4}=2$?

A: Yes, we can use a calculator to solve the equation $-5+\sqrt{x+4}=2$. However, it is always a good idea to verify the solution by plugging it back into the original equation.

Q: What if the equation has a variable inside the square root?

A: If the equation has a variable inside the square root, we need to use a different method to solve the equation. In this case, we need to use algebraic manipulations to isolate the variable.

Conclusion

In this article, we answered some frequently asked questions related to solving the equation $-5+\sqrt{x+4}=2$. We also provided some additional tips and resources for solving equations involving square roots.

Frequently Asked Questions

• Q: What is the first step in solving the equation $-5+\sqrt{x+4}=2$? A: The first step is to isolate the square root term by adding $5$ to both sides of the equation.
• Q: What is the property of square roots that we used to simplify the left-hand side of the equation? A: The property of square roots that we used is $(\sqrt{a})^2=a$.
• Q: How do we verify the solution to the equation? A: We verify the solution by plugging it back into the original equation and checking if it is true.

Additional Resources

• For more information on solving equations involving square roots, see the article "Solving Equations with Square Roots".
• For more practice problems on solving equations involving square roots, see the worksheet "Solving Equations with Square Roots Practice".

References

• [1] "Solving Equations with Square Roots" by Math Open Reference
• [2] "Solving Equations with Square Roots Practice" by Mathway

Related Articles

• Solving Equations with Absolute Values
• Solving Equations with Fractions
• Solving Equations with Exponents