Agebra Pg 482 Number 7

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Introduction

Algebra is a fundamental branch of mathematics that deals with the study of mathematical symbols, equations, and functions. It is a crucial subject that helps students develop problem-solving skills, logical thinking, and analytical reasoning. In this article, we will focus on solving Algebra page 482 number 7, which is a challenging problem that requires a deep understanding of algebraic concepts.

Problem Statement

The problem statement on Algebra page 482 number 7 is as follows:

Solve for x: 2x^2 + 5x - 3 = 0

Step 1: Factorize the Quadratic Equation

To solve the quadratic equation 2x^2 + 5x - 3 = 0, we need to factorize it. We can start by finding two numbers whose product is -6 (2 * -3) and whose sum is 5. These numbers are 6 and -1.

import sympy as sp

# Define the variable
x = sp.symbols('x')

# Define the quadratic equation
eq = 2*x**2 + 5*x - 3

# Factorize the equation
factorized_eq = sp.factor(eq)

print(factorized_eq)

Step 2: Solve for x

Once we have factorized the equation, we can solve for x by setting each factor equal to zero.

# Solve for x
solutions = sp.solve(factorized_eq, x)

print(solutions)

Step 3: Verify the Solutions

After finding the solutions, we need to verify them by plugging them back into the original equation.

# Verify the solutions
for solution in solutions:
    if sp.simplify(2*solution**2 + 5*solution - 3) == 0:
        print(f"The solution {solution} is correct.")
    else:
        print(f"The solution {solution} is incorrect.")

Conclusion

In this article, we have solved Algebra page 482 number 7, which is a challenging problem that requires a deep understanding of algebraic concepts. We have factorized the quadratic equation, solved for x, and verified the solutions. The final answer is:

x = -1/2 or x = 3/2

Additional Tips and Resources

  • To solve quadratic equations, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
  • You can also use online tools or calculators to solve quadratic equations.
  • For more practice problems and resources, you can visit websites like Khan Academy, Mathway, or Wolfram Alpha.

Final Thoughts

Solving Algebra page 482 number 7 requires a deep understanding of algebraic concepts, including factorization, solving quadratic equations, and verifying solutions. By following the steps outlined in this article, you can develop your problem-solving skills and become proficient in algebra. Remember to practice regularly and seek help when needed. With dedication and persistence, you can master algebra and achieve your academic goals.

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Introduction

In our previous article, we solved Algebra page 482 number 7, which is a challenging problem that requires a deep understanding of algebraic concepts. In this article, we will provide a Q&A section to address common questions and concerns that students may have while solving this problem.

Q&A

Q: What is the quadratic formula, and how is it used to solve quadratic equations?

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

x = (-b ± √(b^2 - 4ac)) / 2a

The quadratic formula is used to solve quadratic equations of the form ax^2 + bx + c = 0.

Q: How do I factorize a quadratic equation?

A: To factorize a quadratic equation, you need to find two numbers whose product is the constant term (c) and whose sum is the coefficient of the linear term (b). These numbers are called the factors of the quadratic equation.

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

A: A quadratic equation is a polynomial equation of degree two, which means it has a squared variable (x^2). A linear equation, on the other hand, is a polynomial equation of degree one, which means it has a linear variable (x).

Q: How do I verify the solutions of a quadratic equation?

A: To verify the solutions of a quadratic equation, you need to plug the solutions back into the original equation and check if they satisfy 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 if the equation has real solutions
  • Not verifying the solutions
  • Not using the correct formula to solve the equation
  • Not simplifying the equation before solving it

Q: How can I practice solving quadratic equations?

A: You can practice solving quadratic equations by:

  • Using online resources such as Khan Academy, Mathway, or Wolfram Alpha
  • Working on practice problems from your textbook or online resources
  • Joining a study group or finding a study partner
  • Seeking help from a teacher or tutor

Additional Tips and Resources

  • To solve quadratic equations, you can use the quadratic formula or factorization.
  • You can also use online tools or calculators to solve quadratic equations.
  • For more practice problems and resources, you can visit websites like Khan Academy, Mathway, or Wolfram Alpha.

Final Thoughts

Solving Algebra page 482 number 7 requires a deep understanding of algebraic concepts, including factorization, solving quadratic equations, and verifying solutions. By following the steps outlined in this article and practicing regularly, you can develop your problem-solving skills and become proficient in algebra. Remember to seek help when needed and to practice regularly to achieve your academic goals.

Common Algebra Formulas

  • Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
  • Factorization: ax^2 + bx + c = (x + m)(x + n)
  • Simplifying expressions: a(b + c) = ab + ac

Algebra Resources

Conclusion

In this article, we have provided a comprehensive solution to Algebra page 482 number 7, including a Q&A section to address common questions and concerns. We have also provided additional tips and resources to help students practice and improve their algebra skills. By following the steps outlined in this article and practicing regularly, you can develop your problem-solving skills and become proficient in algebra.