Find The Solutions To $x^2 = 20$.A. $x = \pm 2 \sqrt{5}$ B. $ X = ± 10 2 X = \pm 10 \sqrt{2} X = ± 10 2 ​ [/tex] C. $x = \pm 5 \sqrt{2}$ D. $x = \pm 2 \sqrt{10}$

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Introduction

Solving quadratic equations is a fundamental concept in mathematics, and it is essential to understand the different methods and techniques used to find the solutions. In this article, we will focus on solving the quadratic equation $x^2 = 20$ and explore the different methods used to find the solutions.

Understanding the Quadratic Equation

A quadratic equation is a polynomial equation of degree two, which means that the highest power of the variable is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. In this case, we have a quadratic equation in the form of $x^2 = 20$, where $a = 1$, $b = 0$, and $c = -20$.

Solving the Quadratic Equation

To solve the quadratic equation $x^2 = 20$, we need to find the values of $x$ that satisfy the equation. We can start by taking the square root of both sides of the equation, which gives us $x = \pm \sqrt{20}$. However, we can simplify this further by expressing $\sqrt{20}$ as $\sqrt{4 \times 5}$, which is equal to $2\sqrt{5}$.

Finding the Solutions

Now that we have simplified the equation, we can find the solutions by substituting the value of $x$ back into the original equation. We have two possible solutions: $x = 2\sqrt{5}$ and $x = -2\sqrt{5}$. These are the only two solutions to the quadratic equation $x^2 = 20$.

Comparing the Solutions

Let's compare the solutions we found with the options given in the problem. We have two possible solutions: $x = \pm 2\sqrt{5}$ and $x = \pm 10\sqrt{2}$. However, we can see that the solution $x = \pm 2\sqrt{5}$ is the correct solution to the quadratic equation $x^2 = 20$.

Conclusion

In conclusion, we have solved the quadratic equation $x^2 = 20$ and found the solutions to be $x = \pm 2\sqrt{5}$. We can see that this solution is the correct solution to the equation, and it is the only solution that satisfies the equation.

Frequently Asked Questions

• What is the quadratic equation $x^2 = 20$?
• How do we solve the quadratic equation $x^2 = 20$?
• What are the solutions to the quadratic equation $x^2 = 20$?

Step-by-Step Solution

1. Start by taking the square root of both sides of the equation $x^2 = 20$.
2. Simplify the equation by expressing $\sqrt{20}$ as $\sqrt{4 \times 5}$.
3. Substitute the value of $x$ back into the original equation to find the solutions.
4. Compare the solutions with the options given in the problem.

Final Answer

The final answer is $x = \pm 2\sqrt{5}$.

Discussion

The quadratic equation $x^2 = 20$ is a simple equation that can be solved using basic algebraic techniques. However, it is essential to understand the different methods and techniques used to solve quadratic equations, as they are used extensively in mathematics and other fields.

Related Topics

• Solving quadratic equations using factoring
• Solving quadratic equations using the quadratic formula
• Solving quadratic equations using graphing

References

• [1] "Quadratic Equations" by Math Open Reference
• [2] "Solving Quadratic Equations" by Khan Academy
• [3] "Quadratic Formula" by Wolfram MathWorld

Additional Resources

• [1] "Quadratic Equations" by MIT OpenCourseWare
• [2] "Solving Quadratic Equations" by Purplemath
• [3] "Quadratic Formula" by Mathway

Conclusion

In conclusion, we have solved the quadratic equation $x^2 = 20$ and found the solutions to be $x = \pm 2\sqrt{5}$. We can see that this solution is the correct solution to the equation, and it is the only solution that satisfies the equation.

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Introduction

In our previous article, we solved the quadratic equation $x^2 = 20$ and found the solutions to be $x = \pm 2\sqrt{5}$. In this article, we will answer some of the frequently asked questions related to the quadratic equation $x^2 = 20$.

Q&A

Q1: What is the quadratic equation $x^2 = 20$?

A1: The quadratic equation $x^2 = 20$ is a polynomial equation of degree two, where the highest power of the variable is two. In this case, we have a quadratic equation in the form of $x^2 = 20$, where $a = 1$, $b = 0$, and $c = -20$.

Q2: How do we solve the quadratic equation $x^2 = 20$?

A2: To solve the quadratic equation $x^2 = 20$, we need to find the values of $x$ that satisfy the equation. We can start by taking the square root of both sides of the equation, which gives us $x = \pm \sqrt{20}$. However, we can simplify this further by expressing $\sqrt{20}$ as $\sqrt{4 \times 5}$, which is equal to $2\sqrt{5}$.

Q3: What are the solutions to the quadratic equation $x^2 = 20$?

A3: The solutions to the quadratic equation $x^2 = 20$ are $x = \pm 2\sqrt{5}$. These are the only two solutions to the equation.

Q4: How do we compare the solutions with the options given in the problem?

A4: To compare the solutions with the options given in the problem, we need to substitute the value of $x$ back into the original equation. We have two possible solutions: $x = 2\sqrt{5}$ and $x = -2\sqrt{5}$. However, we can see that the solution $x = \pm 2\sqrt{5}$ is the correct solution to the quadratic equation $x^2 = 20$.

Q5: What are some of the related topics to solving quadratic equations?

A5: Some of the related topics to solving quadratic equations include:

• Solving quadratic equations using factoring
• Solving quadratic equations using the quadratic formula
• Solving quadratic equations using graphing

Q6: What are some of the resources available for learning more about quadratic equations?

A6: Some of the resources available for learning more about quadratic equations include:

• [1] "Quadratic Equations" by Math Open Reference
• [2] "Solving Quadratic Equations" by Khan Academy
• [3] "Quadratic Formula" by Wolfram MathWorld

Q7: How do we use the quadratic formula to solve quadratic equations?

A7: The quadratic formula is a method for solving quadratic equations of the form $ax^2 + bx + c = 0$. The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. We can use this formula to solve quadratic equations by substituting the values of $a$, $b$, and $c$ into the formula.

Q8: What are some of the common mistakes to avoid when solving quadratic equations?

A8: Some of the common mistakes to avoid when solving quadratic equations include:

• Not simplifying the equation before solving it
• Not checking the solutions before accepting them
• Not using the correct method for solving the equation

Conclusion

In conclusion, we have answered some of the frequently asked questions related to the quadratic equation $x^2 = 20$. We hope that this article has been helpful in providing a better understanding of the quadratic equation $x^2 = 20$ and its solutions.

Frequently Asked Questions

• What is the quadratic equation $x^2 = 20$?
• How do we solve the quadratic equation $x^2 = 20$?
• What are the solutions to the quadratic equation $x^2 = 20$?
• How do we compare the solutions with the options given in the problem?
• What are some of the related topics to solving quadratic equations?
• What are some of the resources available for learning more about quadratic equations?
• How do we use the quadratic formula to solve quadratic equations?
• What are some of the common mistakes to avoid when solving quadratic equations?

Step-by-Step Solution

1. Start by taking the square root of both sides of the equation $x^2 = 20$.
2. Simplify the equation by expressing $\sqrt{20}$ as $\sqrt{4 \times 5}$.
3. Substitute the value of $x$ back into the original equation to find the solutions.
4. Compare the solutions with the options given in the problem.
5. Use the quadratic formula to solve quadratic equations.
6. Check the solutions before accepting them.

Final Answer

The final answer is $x = \pm 2\sqrt{5}$.

Discussion

The quadratic equation $x^2 = 20$ is a simple equation that can be solved using basic algebraic techniques. However, it is essential to understand the different methods and techniques used to solve quadratic equations, as they are used extensively in mathematics and other fields.

Related Topics

• Solving quadratic equations using factoring
• Solving quadratic equations using the quadratic formula
• Solving quadratic equations using graphing

References

• [1] "Quadratic Equations" by Math Open Reference
• [2] "Solving Quadratic Equations" by Khan Academy
• [3] "Quadratic Formula" by Wolfram MathWorld

Additional Resources

• [1] "Quadratic Equations" by MIT OpenCourseWare
• [2] "Solving Quadratic Equations" by Purplemath
• [3] "Quadratic Formula" by Mathway