Solve The Equation $11x^2 - 88 = 0$. Round To The Nearest Hundredth.A. $x = \pm 9.31$B. $ X = ± 2.83 X = \pm 2.83 X = ± 2.83 [/tex]C. $x = \pm 5.69$D. $x = \pm 3.32$
Introduction
Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving the quadratic equation $11x^2 - 88 = 0$ and provide a step-by-step guide on how to approach it.
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (in this case, x) is two. The general form of a quadratic equation is $ax^2 + bx + c = 0$, where a, b, and c are constants. Quadratic equations can be solved using various methods, including factoring, the quadratic formula, and graphing.
The Quadratic Formula
The quadratic formula is a powerful tool for solving quadratic equations. It is given by:
where a, b, and c are the coefficients of the quadratic equation. To use the quadratic formula, we need to identify the values of a, b, and c in the given equation.
Solving the Equation $11x^2 - 88 = 0$
Let's apply the quadratic formula to solve the equation $11x^2 - 88 = 0$. We can rewrite the equation as $11x^2 = 88$, and then divide both sides by 11 to get $x^2 = 8$.
Now, we can take the square root of both sides to get $x = \pm \sqrt{8}$. Using a calculator, we can find the value of $\sqrt{8}$ to be approximately 2.83.
Therefore, the solutions to the equation $11x^2 - 88 = 0$ are $x = \pm 2.83$.
Rounding to the Nearest Hundredth
The problem asks us to round the solutions to the nearest hundredth. To do this, we need to look at the thousandths place of the decimal. In this case, the thousandths place is 3, which is less than 5. Therefore, we round down to 2.83.
Conclusion
In this article, we solved the quadratic equation $11x^2 - 88 = 0$ using the quadratic formula. We found the solutions to be $x = \pm 2.83$ and rounded them to the nearest hundredth. This problem demonstrates the importance of using the quadratic formula to solve quadratic equations and the need to round solutions to the nearest hundredth.
Comparison of Solutions
Let's compare our solution to the options provided:
- A. $x = \pm 9.31$: This is not a correct solution.
- B. $x = \pm 2.83$: This is the correct solution.
- C. $x = \pm 5.69$: This is not a correct solution.
- D. $x = \pm 3.32$: This is not a correct solution.
Therefore, the correct answer is B. $x = \pm 2.83$.
Final Thoughts
Introduction
In our previous article, we solved the quadratic equation $11x^2 - 88 = 0$ using the quadratic formula. In this article, we will answer some frequently asked questions about quadratic equations and provide additional guidance on how to approach them.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is a polynomial equation of degree one, which means the highest power of the variable (in this case, x) is one. A quadratic equation, on the other hand, is a polynomial equation of degree two, which means the highest power of the variable (in this case, x) is two.
Q: How do I know if a quadratic equation can be factored?
A: To determine if a quadratic equation can be factored, you need to look at the coefficients of the equation. If the coefficients are integers and the equation can be written in the form of , then the equation can be factored.
Q: What is the quadratic formula and how do I use it?
A: The quadratic formula is a powerful tool for solving quadratic equations. It is given by:
where a, b, and c are the coefficients of the quadratic equation. To use the quadratic formula, you need to identify the values of a, b, and c in the given equation and plug them into the formula.
Q: What is the difference between the quadratic formula and the square root method?
A: The quadratic formula and the square root method are two different methods for solving quadratic equations. The quadratic formula is a general method that can be used to solve any quadratic equation, while the square root method is a specific method that can be used to solve quadratic equations that can be written in the form of .
Q: How do I round solutions to the nearest hundredth?
A: To round solutions to the nearest hundredth, you need to look at the thousandths place of the decimal. If the thousandths place is 5 or greater, you round up. If the thousandths place is less than 5, you round down.
Q: What are some common mistakes to avoid when solving quadratic equations?
A: Some common mistakes to avoid when solving quadratic equations include:
- Not identifying the values of a, b, and c in the given equation
- Not plugging the values of a, b, and c into the quadratic formula
- Not simplifying the expression under the square root
- Not rounding solutions to the nearest hundredth
Q: How do I check my solutions to a quadratic equation?
A: To check your solutions to a quadratic equation, you need to plug the solutions back into the original equation and verify that they are true. If the solutions are true, then you have found the correct solutions.
Conclusion
In this article, we answered some frequently asked questions about quadratic equations and provided additional guidance on how to approach them. By following the steps outlined in this article, you can become proficient in solving quadratic equations and avoid common mistakes.
Additional Resources
For more information on quadratic equations, we recommend the following resources:
- Khan Academy: Quadratic Equations
- Mathway: Quadratic Equations
- Wolfram Alpha: Quadratic Equations
Final Thoughts
Solving quadratic equations is an essential skill in mathematics, and the quadratic formula is a powerful tool for solving them. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving quadratic equations and achieve success in mathematics.