How to Solve Quadratic Equations by Completing the Square? Grade 9 Math

MATH TEACHER GON
22 Aug 202206:32

Summary

TLDRIn this educational video, the teacher guides viewers through solving quadratic equations using the method of completing the square. Starting with the equation x^2 + 6x - 2 = 0, the tutorial demonstrates transposing constants, adding a term to form a perfect square trinomial, and then expressing it as a square of a binomial. The process concludes with extracting square roots to find the values of x, resulting in x = ±√11 - 3. The video promises a follow-up on handling equations with coefficients greater than one, encouraging viewers to stay tuned.

Takeaways

  • 📚 The video discusses solving quadratic equations by completing the square, an alternative to factoring and extracting square roots.
  • 🔗 Links to previous videos on factoring and square root extraction are promised in the description box for continuity.
  • 📉 The example equation given is x^2 + 6x - 2 = 0, which is challenging to factor, hence the focus on completing the square.
  • ➡️ The first step in completing the square is to transpose the constant term to the other side of the equation, resulting in x^2 + 6x = 2.
  • 🔢 To form a perfect square trinomial, calculate the value of b/2, square it, and add it to both sides of the equation, leading to x^2 + 6x + 9 = 11.
  • 🟣 The expression is then rewritten as a square of a binomial, (x + 3)^2 = 11.
  • 📐 Extracting the square roots gives x + 3 = ±√11, introducing the concept of both positive and negative solutions.
  • 🔄 Isolating the variable x involves moving the +3 to the other side, resulting in x = -3 ± √11.
  • 📝 The solutions to the equation are x1 = √11 - 3 and x2 = -√11 - 3, demonstrating the use of both positive and negative square roots.
  • 🎥 The video concludes with a teaser for another video that will cover cases where the coefficient of the first term is greater than one.

Q & A

  • What is the main topic discussed in the video?

    -The main topic discussed in the video is solving quadratic equations by completing the square.

  • Why is completing the square a useful method for solving quadratic equations?

    -Completing the square is useful when the quadratic equation is difficult to factor, as it provides an alternative method to find the solutions.

  • What is the first step in completing the square for a quadratic equation with a leading coefficient of 1?

    -The first step is to transpose the constant term to the other side of the equation, changing its sign in the process.

  • How do you determine the third term to make the expression a perfect square trinomial?

    -You take the coefficient of the linear term (b), divide it by 2, and then square the result to get the third term.

  • What is the purpose of expressing the perfect square trinomial as a square of a binomial?

    -Expressing it as a square of a binomial simplifies the equation and allows for the extraction of square roots to solve for x.

  • How do you isolate the variable x when completing the square?

    -You isolate x by removing the linear term (if present) from the equation and transposing it to the other side.

  • What is the significance of the number 11 in the video's example?

    -In the example, 11 is the sum of the constant term and the square of the number obtained from the linear term's coefficient divided by 2.

  • Why is it necessary to consider both the positive and negative square roots when solving for x?

    -Considering both the positive and negative square roots ensures that all possible solutions for x are found, as square roots can have both positive and negative values.

  • How many solutions does the quadratic equation presented in the video have?

    -The quadratic equation presented in the video has two solutions, x₁ and x₂.

  • What is the final form of the solutions for x in the example given in the video?

    -The final form of the solutions for x are x = √11 - 3 and x = -√11 - 3.

  • What is the advice given for viewers who are new to the channel?

    -The advice for new viewers is to like, subscribe, and hit the bell button to stay updated with the latest uploads.

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MathematicsQuadratic EquationsCompleting the SquareEducational ContentAlgebraSolving EquationsMath TutorialTeacher's GuideMath StrategiesEducational Video
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