Find The Solution Set For The Equation $r^2 = 16$.Separate The Two Values With A Comma.

Introduction

In mathematics, equations are a fundamental concept that help us solve problems and understand various mathematical concepts. One of the most common types of equations is the quadratic equation, which is in the form of $ax^2 + bx + c = 0$. However, in this article, we will be dealing with a simpler equation, $r^2 = 16$, where we need to find the solution set for the variable $r$. The solution set is the set of all possible values of $r$ that satisfy the given equation.

Understanding the Equation

The equation $r^2 = 16$ is a quadratic equation in disguise. It can be rewritten as $r^2 - 16 = 0$, which is a quadratic equation in the form of $ax^2 + bx + c = 0$. In this case, $a = 1$, $b = 0$, and $c = -16$. To solve this equation, we can use the quadratic formula, which is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Solving the Equation

However, in this case, we can solve the equation by taking the square root of both sides. This gives us $r = \pm \sqrt{16}$. Since $\sqrt{16} = 4$, we have $r = \pm 4$. Therefore, the solution set for the equation $r^2 = 16$ is $r = -4, 4$.

Separating the Values

As per the problem statement, we need to separate the two values with a comma. Therefore, the solution set for the equation $r^2 = 16$ is $r = -4, 4$.

Conclusion

In this article, we have found the solution set for the equation $r^2 = 16$. We have used the concept of quadratic equations and the square root to solve the equation. The solution set is $r = -4, 4$, which are the two values that satisfy the given equation.

Additional Information

It's worth noting that the equation $r^2 = 16$ has two solutions, $r = -4$ and $r = 4$. This is because the square of both $-4$ and $4$ is equal to $16$. Therefore, both values satisfy the given equation.

Real-World Applications

The equation $r^2 = 16$ has several real-world applications. For example, in physics, the equation can be used to describe the motion of an object under the influence of gravity. In engineering, the equation can be used to design and analyze the stability of structures such as bridges and buildings.

Final Thoughts

In conclusion, the solution set for the equation $r^2 = 16$ is $r = -4, 4$. This equation has several real-world applications and can be used to solve problems in various fields such as physics and engineering.

Frequently Asked Questions

• Q: What is the solution set for the equation $r^2 = 16$? A: The solution set for the equation $r^2 = 16$ is $r = -4, 4$.
• Q: How do I solve the equation $r^2 = 16$? A: You can solve the equation by taking the square root of both sides, which gives you $r = \pm \sqrt{16}$.
• Q: What are the real-world applications of the equation $r^2 = 16$? A: The equation $r^2 = 16$ has several real-world applications, including physics and engineering.

References

• [1] "Quadratic Equations" by Math Open Reference
• [2] "Square Root" by Khan Academy
• [3] "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca

Related Articles

• [1] "Solving Quadratic Equations"
• [2] "Understanding Square Roots"
• [3] "Real-World Applications of Quadratic Equations"
  

Introduction

In our previous article, we discussed how to solve the equation $r^2 = 16$ and found the solution set to be $r = -4, 4$. However, we know that there are many more questions that our readers may have about this equation. In this article, we will address some of the most frequently asked questions about solving the equation $r^2 = 16$.

Q&A

Q: What is the solution set for the equation $r^2 = 16$?

A: The solution set for the equation $r^2 = 16$ is $r = -4, 4$. This means that both $-4$ and $4$ are solutions to the equation.

Q: How do I solve the equation $r^2 = 16$?

A: To solve the equation $r^2 = 16$, you can take the square root of both sides, which gives you $r = \pm \sqrt{16}$. Since $\sqrt{16} = 4$, you have $r = \pm 4$.

Q: What are the real-world applications of the equation $r^2 = 16$?

A: The equation $r^2 = 16$ has several real-world applications, including physics and engineering. For example, in physics, the equation can be used to describe the motion of an object under the influence of gravity. In engineering, the equation can be used to design and analyze the stability of structures such as bridges and buildings.

Q: Can I use the quadratic formula to solve the equation $r^2 = 16$?

A: Yes, you can use the quadratic formula to solve the equation $r^2 = 16$. The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. In this case, $a = 1$, $b = 0$, and $c = -16$. Plugging these values into the quadratic formula, you get $r = \frac{0 \pm \sqrt{0^2 - 4(1)(-16)}}{2(1)} = \pm 4$.

Q: What is the difference between the equation $r^2 = 16$ and the equation $r^2 = -16$?

A: The equation $r^2 = -16$ has no real solutions, because the square of any real number is always non-negative. In contrast, the equation $r^2 = 16$ has two real solutions, $r = -4$ and $r = 4$.

Q: Can I use the equation $r^2 = 16$ to solve other equations?

A: Yes, you can use the equation $r^2 = 16$ to solve other equations that are in the form of $r^2 = k$, where $k$ is a constant. For example, if you have the equation $r^2 = 9$, you can use the equation $r^2 = 16$ to find the solution set.

Q: What are some common mistakes to avoid when solving the equation $r^2 = 16$?

A: Some common mistakes to avoid when solving the equation $r^2 = 16$ include:

• Not taking the square root of both sides of the equation
• Not considering both the positive and negative solutions
• Not checking the validity of the solutions

Conclusion

In this article, we have addressed some of the most frequently asked questions about solving the equation $r^2 = 16$. We hope that this article has been helpful in clarifying any doubts that you may have had about this equation. If you have any further questions, please don't hesitate to ask.

Additional Resources

• [1] "Quadratic Equations" by Math Open Reference
• [2] "Square Root" by Khan Academy
• [3] "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca

Related Articles

• [1] "Solving Quadratic Equations"
• [2] "Understanding Square Roots"
• [3] "Real-World Applications of Quadratic Equations"