Find The Solution For X When X 2 = 1.69 X^2=1.69 X 2 = 1.69 .A. X = 1.3 X=1.3 X = 1.3 B. X = 0.13 X=0.13 X = 0.13 C. X = ± 1.3 X= \pm 1.3 X = ± 1.3 D. X = ± 0.13 X= \pm 0.13 X = ± 0.13

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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 a specific quadratic equation, x2=1.69x^2=1.69, and explore the different methods and techniques used to find the value of x.

Understanding Quadratic Equations

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 ax2+bx+c=0ax^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:

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

In our case, the quadratic equation is x2=1.69x^2=1.69, which can be rewritten as x2−1.69=0x^2-1.69=0. Comparing this with the general form of a quadratic equation, we have a=1, b=0, and c=-1.69.

Applying the Quadratic Formula

Now that we have identified the values of a, b, and c, we can plug them into the quadratic formula:

x=−0±02−4(1)(−1.69)2(1)x=\frac{-0\pm\sqrt{0^2-4(1)(-1.69)}}{2(1)}

Simplifying the expression, we get:

x=±6.762x=\frac{\pm\sqrt{6.76}}{2}

x=±2.62x=\frac{\pm2.6}{2}

x=±1.3x=\pm1.3

Interpreting the Results

We have found that the solutions to the quadratic equation x2=1.69x^2=1.69 are x=±1.3x=\pm1.3. This means that the value of x can be either 1.3 or -1.3.

Conclusion

In this article, we have solved the quadratic equation x2=1.69x^2=1.69 using the quadratic formula. We have found that the solutions to the equation are x=±1.3x=\pm1.3. This demonstrates the importance of quadratic equations in mathematics and the need for accurate and efficient methods for solving them.

Final Answer

The final answer to the problem is:

  • A. x=1.3x=1.3 is incorrect, as the solution is x=±1.3x=\pm1.3.
  • B. x=0.13x=0.13 is incorrect, as the solution is x=±1.3x=\pm1.3.
  • C. x=±1.3x= \pm 1.3 is correct.
  • D. x=±0.13x= \pm 0.13 is incorrect, as the solution is x=±1.3x=\pm1.3.

Additional Tips and Tricks

  • When solving quadratic equations, it is essential to identify the values of a, b, and c correctly.
  • The quadratic formula is a powerful tool for solving quadratic equations, but it may not always be the most efficient method.
  • Graphing and factoring are alternative methods for solving quadratic equations, and they can be useful in certain situations.

Real-World Applications

Quadratic equations have numerous real-world applications, 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 economic systems and make predictions about future trends.

Conclusion

In conclusion, solving quadratic equations is a crucial skill for students and professionals alike. The quadratic formula is a powerful tool for solving quadratic equations, but it may not always be the most efficient method. By understanding the different methods and techniques used to solve quadratic equations, we can gain a deeper appreciation for the beauty and complexity of mathematics.

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, covering topics such as solving quadratic equations, graphing quadratic functions, and real-world applications.

Q1: 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 ax2+bx+c=0ax^2+bx+c=0, where a, b, and c are constants.

Q2: How do I solve a quadratic equation?

There are several methods for solving quadratic equations, including factoring, the quadratic formula, and graphing. The quadratic formula is a powerful tool for solving quadratic equations and is given by:

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

Q3: What is the quadratic formula?

The quadratic formula is a formula for solving quadratic equations. It is given by:

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

Q4: How do I graph a quadratic function?

To graph a quadratic function, you can use a graphing calculator or software, or you can plot the function by hand. The graph of a quadratic function is a parabola, which is a U-shaped curve.

Q5: What are some real-world applications of quadratic equations?

Quadratic equations have numerous real-world applications, 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 economic systems and make predictions about future trends.

Q6: Can I use a calculator to solve quadratic equations?

Yes, you can use a calculator to solve quadratic equations. Most graphing calculators and software have built-in functions for solving quadratic equations.

Q7: What is the difference between a quadratic equation and a linear equation?

A quadratic equation is a polynomial equation of degree two, while a linear equation is a polynomial equation of degree one. The general form of a linear equation is ax+b=0ax+b=0, where a and b are constants.

Q8: Can I solve a quadratic equation by factoring?

Yes, you can solve a quadratic equation by factoring. Factoring involves expressing the quadratic equation as a product of two binomials.

Q9: What is the discriminant in the quadratic formula?

The discriminant is the expression under the square root in the quadratic formula, which is b2−4acb^2-4ac. The discriminant determines the nature of the solutions to the quadratic equation.

Q10: Can I use the quadratic formula to solve a quadratic equation with complex solutions?

Yes, you can use the quadratic formula to solve a quadratic equation with complex solutions. The quadratic formula will give you two complex solutions.

Conclusion

In conclusion, quadratic equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. By understanding the different methods and techniques used to solve quadratic equations, we can gain a deeper appreciation for the beauty and complexity of mathematics.

Additional Resources

  • For more information on quadratic equations, visit the Khan Academy website.
  • For more information on graphing quadratic functions, visit the Mathway website.
  • For more information on real-world applications of quadratic equations, visit the Wolfram Alpha website.

Final Tips and Tricks

  • When solving quadratic equations, it is essential to identify the values of a, b, and c correctly.
  • The quadratic formula is a powerful tool for solving quadratic equations, but it may not always be the most efficient method.
  • Graphing and factoring are alternative methods for solving quadratic equations, and they can be useful in certain situations.