Select The Correct Answer.What Are The Solutions To This Equation? 7 X 2 − 28 = 0 7x^2 - 28 = 0 7 X 2 − 28 = 0 A. X = − 2 X = -2 X = − 2 And X = 2 X = 2 X = 2 B. X = − 4 X = -4 X = − 4 And X = 4 X = 4 X = 4 C. X = − 7 X = -\sqrt{7} X = − 7 ​ And X = 7 X = \sqrt{7} X = 7 ​ D. $x =

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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 quadratic equations of the form ax2+bx+c=0ax^2 + bx + c = 0, where aa, bb, and cc are constants. We will use the given equation 7x2−28=07x^2 - 28 = 0 as an example to demonstrate the steps involved in solving quadratic equations.

Understanding the Equation

The given equation is 7x2−28=07x^2 - 28 = 0. To solve this equation, we need to isolate the variable xx. The first step is to add 2828 to both sides of the equation to get rid of the negative term.

7x^2 - 28 + 28 = 0 + 28

This simplifies to:

7x^2 = 28

Dividing by the Coefficient

The next step is to divide both sides of the equation by the coefficient of x2x^2, which is 77. This will isolate the term with x2x^2.

\frac{7x^2}{7} = \frac{28}{7}

This simplifies to:

x^2 = 4

Taking the Square Root

To solve for xx, we need to take the square root of both sides of the equation. This will give us two possible values for xx.

x = \pm \sqrt{4}

This simplifies to:

x = \pm 2

Solutions to the Equation

Therefore, the solutions to the equation 7x2−28=07x^2 - 28 = 0 are x=−2x = -2 and x=2x = 2.

Conclusion

In this article, we have demonstrated the steps involved in solving quadratic equations. We have used the given equation 7x2−28=07x^2 - 28 = 0 as an example to illustrate the process. By following these steps, we can solve quadratic equations and find the values of the variable xx.

Answer

The correct answer to the equation 7x2−28=07x^2 - 28 = 0 is:

A. x=−2x = -2 and x=2x = 2

This is the only option that matches the solutions we obtained in the previous section.

Discussion

Quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we have demonstrated the steps involved in solving quadratic equations. We have used the given equation 7x2−28=07x^2 - 28 = 0 as an example to illustrate the process. By following these steps, we can solve quadratic equations and find the values of the variable xx.

What are the Solutions to this Equation?

The solutions to the equation 7x2−28=07x^2 - 28 = 0 are x=−2x = -2 and x=2x = 2.

How to Solve Quadratic Equations

To solve quadratic equations, we need to follow these steps:

  1. Add or subtract the constant term to isolate the term with x2x^2.
  2. Divide both sides of the equation by the coefficient of x2x^2.
  3. Take the square root of both sides of the equation.
  4. Simplify the expression to obtain the values of the variable xx.

Why is it Important to Solve Quadratic Equations?

Solving quadratic equations is an important skill for students and professionals alike. It is used in a wide range of applications, including physics, engineering, and economics. By solving quadratic equations, we can model real-world problems and make predictions about the behavior of systems.

What are the Applications of Quadratic Equations?

Quadratic equations have a wide range of applications in various fields, including:

  • Physics: Quadratic equations are used to model the motion of objects under the influence of gravity.
  • Engineering: Quadratic equations are used to design and optimize systems, such as bridges and buildings.
  • Economics: Quadratic equations are used to model the behavior of economic systems and make predictions about the future.

Conclusion

In conclusion, solving quadratic equations is an important skill for students and professionals alike. By following the steps outlined in this article, we can solve quadratic equations and find the values of the variable xx. Quadratic equations have a wide range of applications in various fields, including physics, engineering, and economics.

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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 answer some of the most frequently asked questions about quadratic equations.

Q: What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree two, which means that the highest power of the variable is two. It is typically written in the form ax2+bx+c=0ax^2 + bx + c = 0, where aa, bb, and cc are constants.

Q: How to Solve Quadratic Equations?

To solve quadratic equations, we need to follow these steps:

  1. Add or subtract the constant term to isolate the term with x2x^2.
  2. Divide both sides of the equation by the coefficient of x2x^2.
  3. Take the square root of both sides of the equation.
  4. Simplify the expression to obtain the values of the variable xx.

Q: What are the Solutions to a Quadratic Equation?

The solutions to a quadratic equation are the values of the variable xx that satisfy the equation. These solutions can be real or complex numbers.

Q: How to Find the Solutions to a Quadratic Equation?

To find the solutions to a quadratic equation, we need to use the quadratic formula:

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

This formula gives us two possible solutions for the variable xx.

Q: What is the Quadratic Formula?

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

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Q: How to Use the Quadratic Formula?

To use the quadratic formula, we need to plug in the values of aa, bb, and cc into the formula. This will give us the solutions to the quadratic equation.

Q: What are the Applications of Quadratic Equations?

Quadratic equations have a wide range of applications in various fields, including:

  • Physics: Quadratic equations are used to model the motion of objects under the influence of gravity.
  • Engineering: Quadratic equations are used to design and optimize systems, such as bridges and buildings.
  • Economics: Quadratic equations are used to model the behavior of economic systems and make predictions about the future.

Q: Why is it Important to Solve Quadratic Equations?

Solving quadratic equations is an important skill for students and professionals alike. It is used in a wide range of applications, including physics, engineering, and economics. By solving quadratic equations, we can model real-world problems and make predictions about the behavior of systems.

Q: What are the Different Types of Quadratic Equations?

There are several types of quadratic equations, including:

  • Monic quadratic equations: These are quadratic equations where the coefficient of x2x^2 is 1.
  • Non-monic quadratic equations: These are quadratic equations where the coefficient of x2x^2 is not 1.
  • Complex quadratic equations: These are quadratic equations that have complex solutions.

Q: How to Graph Quadratic Equations?

To graph quadratic equations, we need to use a graphing calculator or a computer program. We can also use a graphing app on our phone or tablet.

Conclusion

In conclusion, quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. By following the steps outlined in this article, we can solve quadratic equations and find the values of the variable xx. Quadratic equations have a wide range of applications in various fields, including physics, engineering, and economics.

Frequently Asked Questions

  • 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 is two.
  • Q: How to solve quadratic equations?
  • A: To solve quadratic equations, we need to follow these steps: add or subtract the constant term to isolate the term with x2x^2, divide both sides of the equation by the coefficient of x2x^2, take the square root of both sides of the equation, and simplify the expression to obtain the values of the variable xx.
  • Q: What are the solutions to a quadratic equation?
  • A: The solutions to a quadratic equation are the values of the variable xx that satisfy the equation.
  • Q: How to find the solutions to a quadratic equation?
  • A: To find the solutions to a quadratic equation, we need to use the quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Additional Resources

  • Quadratic equation calculator: This is a online tool that can help us solve quadratic equations.
  • Quadratic equation solver: This is a software program that can help us solve quadratic equations.
  • Quadratic equation grapher: This is a tool that can help us graph quadratic equations.

Conclusion

In conclusion, quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. By following the steps outlined in this article, we can solve quadratic equations and find the values of the variable xx. Quadratic equations have a wide range of applications in various fields, including physics, engineering, and economics.