Solve The Equation: $x^2 + 9x = 0$Answer: $x = \square$Write Your Answers As A List Of Integers Or Reduced Fractions, With Your Answers Separated By Commas. For Example, If You Get 4 And $-\frac{2}{3}$ As Your Answers, Then

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Introduction

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving the quadratic equation $x^2 + 9x = 0$. This equation is a classic example of a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. Our goal is to find the values of $x$ that satisfy this equation.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at its structure. The equation $x^2 + 9x = 0$ consists of a quadratic term ($x^2$) and a linear term ($9x$). The constant term is zero, which means that the equation has no constant term. This makes the equation a bit simpler to solve, but it still requires some careful manipulation.

Factoring the Equation

One way to solve the equation $x^2 + 9x = 0$ is to factor it. Factoring involves expressing the equation as a product of two binomials. In this case, we can factor the equation as follows:

$x^2 + 9x = 0$

$x(x + 9) = 0$

This tells us that either $x = 0$ or $x + 9 = 0$. We can solve each of these equations separately to find the values of $x$.

Solving for $x$

Let's start by solving the equation $x + 9 = 0$. To do this, we can subtract 9 from both sides of the equation:

$x + 9 = 0$

$x = -9$

So, one solution to the equation is $x = -9$.

Solving for $x$ (continued)

Now, let's solve the equation $x = 0$. This equation is already solved, and we can see that $x = 0$ is a solution to the equation.

Combining the Solutions

We have found two solutions to the equation: $x = -9$ and $x = 0$. These solutions are distinct, and they satisfy the equation $x^2 + 9x = 0$. Therefore, the final answer to the equation is:

$x = -9, 0$

Conclusion

In this article, we solved the quadratic equation $x^2 + 9x = 0$. We used factoring to express the equation as a product of two binomials and then solved each of the resulting equations separately. Our final answer was $x = -9, 0$, which are the two distinct solutions to the equation.

Frequently Asked Questions

• What is a quadratic equation? A quadratic equation is a polynomial equation of degree two, which means that the highest power of the variable (in this case, $x$) is two.
• How do I solve a quadratic equation? There are several methods for solving quadratic equations, including factoring, using the quadratic formula, and graphing. In this article, we used factoring to solve the equation $x^2 + 9x = 0$.
• What is the quadratic formula? The quadratic formula is a formula that can be used to solve quadratic equations. It is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Additional Resources

• Quadratic Equations Tutorial This tutorial provides a comprehensive introduction to quadratic equations, including how to solve them using factoring, the quadratic formula, and graphing.
• Quadratic Formula Calculator This calculator can be used to solve quadratic equations using the quadratic formula.
• Quadratic Equation Solver This solver can be used to solve quadratic equations using factoring, the quadratic formula, and graphing.

Final Answer

The final answer to the equation $x^2 + 9x = 0$ is:

$x = -9, 0$

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Introduction

In our previous article, we solved the quadratic equation $x^2 + 9x = 0$ using factoring. We found that the solutions to the equation are $x = -9$ and $x = 0$. In this article, we will answer some frequently asked questions about quadratic equations and provide additional resources for further learning.

Q&A

Q: What is a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means that the highest power of the variable (in this case, $x$) is two.

Q: How do I solve a quadratic equation?

A: There are several methods for solving quadratic equations, including factoring, using the quadratic formula, and graphing. In our previous article, we used factoring to solve the equation $x^2 + 9x = 0$.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that can be used to solve quadratic equations. It is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to identify the coefficients $a$, $b$, and $c$ in the quadratic equation. Then, you can plug these values into the formula and simplify to find the solutions.

Q: What are the steps to solve a quadratic equation using the quadratic formula?

A: The steps to solve a quadratic equation using the quadratic formula are:

1. Identify the coefficients $a$, $b$, and $c$ in the quadratic equation.
2. Plug these values into the quadratic formula.
3. Simplify the expression to find the solutions.

Q: Can I use the quadratic formula to solve any quadratic equation?

A: Yes, the quadratic formula can be used to solve any quadratic equation. However, it may not always be the easiest or most efficient method, especially for simple equations that can be solved using factoring.

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 coefficients $a$, $b$, and $c$ correctly.
• Not simplifying the expression correctly.
• Not checking the solutions to make sure they are valid.

Q: How do I check my solutions to make sure they are valid?

A: To check your solutions, you can plug them back into the original equation to make sure they satisfy the equation. You can also use the quadratic formula to check your solutions.

Additional Resources

• Quadratic Equations Tutorial This tutorial provides a comprehensive introduction to quadratic equations, including how to solve them using factoring, the quadratic formula, and graphing.
• Quadratic Formula Calculator This calculator can be used to solve quadratic equations using the quadratic formula.
• Quadratic Equation Solver This solver can be used to solve quadratic equations using factoring, the quadratic formula, and graphing.

Conclusion

In this article, we answered some frequently asked questions about quadratic equations and provided additional resources for further learning. We hope this article has been helpful in clarifying any confusion about quadratic equations and how to solve them.

Final Answer

The final answer to the equation $x^2 + 9x = 0$ is:

$x = -9, 0$

We hope this article has been helpful in solving the quadratic equation $x^2 + 9x = 0$. If you have any further questions or need additional help, please don't hesitate to ask.