What Is The First Step In Solving The Equation $x^2-\frac{16}{25}=0$?□What Is The Second Step In Solving The Equation?□

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 explore the first and second steps in solving the equation $x^2-\frac{16}{25}=0$. We will break down the solution into manageable steps, making it easier to understand and apply.

Understanding the Equation

The given equation is a quadratic equation in the form of $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants. In this case, the equation is $x^2 - \frac{16}{25} = 0$. The first step in solving this equation is to isolate the variable, which means getting all the terms with the variable $x$ on one side of the equation.

Step 1: Add $\frac{16}{25}$ to Both Sides

To isolate the variable, we need to add $\frac{16}{25}$ to both sides of the equation. This will give us:

$x^2 = \frac{16}{25}$

By adding $\frac{16}{25}$ to both sides, we have effectively isolated the variable $x$ on the left-hand side of the equation.

Step 2: Take the Square Root of Both Sides

The next step is to take the square root of both sides of the equation. This will give us:

$x = \pm \sqrt{\frac{16}{25}}$

By taking the square root of both sides, we have effectively solved for the variable $x$.

Simplifying the Square Root

The square root of $\frac{16}{25}$ can be simplified as follows:

$\sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}$

Therefore, the solution to the equation is:

$x = \pm \frac{4}{5}$

Conclusion

In conclusion, the first step in solving the equation $x^2 - \frac{16}{25} = 0$ is to add $\frac{16}{25}$ to both sides of the equation, which isolates the variable $x$. The second step is to take the square root of both sides of the equation, which gives us the solution $x = \pm \frac{4}{5}$. By following these steps, we can solve quadratic equations and gain a deeper understanding of this fundamental concept in mathematics.

Additional Tips and Resources

• To solve quadratic equations, it's essential to have a solid understanding of algebraic manipulations and the properties of square roots.
• When solving quadratic equations, it's crucial to check the solutions to ensure they are valid and make sense in the context of the problem.
• For more practice and resources on solving quadratic equations, check out the following websites:
  • Khan Academy: Quadratic Equations
  • Mathway: Quadratic Equations
  • Wolfram Alpha: Quadratic Equations

Frequently Asked Questions

• Q: What is the first step in solving the equation $x^2 - \frac{16}{25} = 0$? A: The first step is to add $\frac{16}{25}$ to both sides of the equation.
• Q: What is the second step in solving the equation $x^2 - \frac{16}{25} = 0$? A: The second step is to take the square root of both sides of the equation.
• Q: What is the solution to the equation $x^2 - \frac{16}{25} = 0$? A: The solution is $x = \pm \frac{4}{5}$.
  Quadratic Equations Q&A: Frequently Asked Questions =====================================================

Introduction

Quadratic equations are a fundamental concept in mathematics, and solving them can be a challenging task for many students and professionals. In this article, we will address some of the most frequently asked questions about quadratic equations, providing clear and concise answers to help you better understand this important topic.

Q: What is a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. It is typically written in the form of $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use various methods, including factoring, the quadratic formula, and completing the square. The method you choose will depend on the specific equation and your personal preference.

Q: What is the quadratic formula?

A: The quadratic formula is a mathematical formula that provides the solutions to a quadratic equation. It is written as:

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

Q: How do I use the quadratic formula?

A: To use the quadratic formula, you need to plug in the values of $a$, $b$, and $c$ from the quadratic equation into the formula. Then, simplify the expression and solve for $x$.

Q: What is the difference between a quadratic equation and a linear equation?

A: A quadratic equation is a polynomial equation of degree two, while a linear equation is a polynomial equation of degree one. In other words, a quadratic equation has a squared variable, while a linear equation does not.

Q: Can I solve a quadratic equation by graphing?

A: Yes, you can solve a quadratic equation by graphing. By graphing the quadratic function, you can find the x-intercepts, which represent the solutions to the equation.

Q: What is the significance of the discriminant in a quadratic equation?

A: The discriminant is the expression under the square root in the quadratic formula. It determines the nature of the solutions to the equation. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has no real solutions.

Q: Can I use a calculator to solve a quadratic equation?

A: Yes, you can use a calculator to solve a quadratic equation. Most calculators have a built-in quadratic formula function that you can use to solve the equation.

Q: What are some common mistakes to avoid when solving quadratic equations?

A: Some common mistakes to avoid when solving quadratic equations include:

• Not checking the solutions to ensure they are valid
• Not simplifying the expression correctly
• Not using the correct method for solving the equation
• Not considering the nature of the solutions (real or complex)

Conclusion

In conclusion, quadratic equations are a fundamental concept in mathematics, and solving them requires a solid understanding of algebraic manipulations and the properties of quadratic functions. By addressing some of the most frequently asked questions about quadratic equations, we hope to have provided you with a better understanding of this important topic.

Additional Resources

• Khan Academy: Quadratic Equations
• Mathway: Quadratic Equations
• Wolfram Alpha: Quadratic Equations
• MIT OpenCourseWare: Quadratic Equations

Frequently Asked Questions (FAQs)

• Q: What is the quadratic formula? A: The quadratic formula is a mathematical formula that provides the solutions to a quadratic equation.
• Q: How do I use the quadratic formula? A: To use the quadratic formula, you need to plug in the values of $a$, $b$, and $c$ from the quadratic equation into the formula.
• Q: What is the difference between a quadratic equation and a linear equation? A: A quadratic equation is a polynomial equation of degree two, while a linear equation is a polynomial equation of degree one.