Solving Quadratic Equation by Completing the Square.pptx

Solving Quadratic Equation by Completing the Square is another method of solving quadratic equation when the equation cannot be solved using factoring and extracting the square root.

1. Warm – Up! Factor the following quadratic trinomial: 1. 2.  

2. Lesson 4: Solving Quadratic Equations by Completing the Square

3. What is It If the quadratic equation 𝑎𝑥 2 +𝑏𝑥+𝑐=0 is NOT factorable into two binomials, roots can be derived by using completing the square method . This process involves getting the 3rd term of the perfect square trinomial by squaring the half of the coefficient of the middle term, 𝑏𝑥, in symbols, 𝒂𝒙 𝟐 +𝒃𝒙+( ) 𝟐 =−𝒄+( ) 𝟐    

4. What is It A perfect square trinomial is  a trinomial that can be written as the square of a binomial . Is the result of squaring a binomial that is the square of the first term added to twice the product of the two terms and the square of the last term.

5. Perfect Square Trinomials Examples x 2 + 6x + 9 x 2 - 10x + 25 x 2 + 12x + 36

6. Creating a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. X 2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2) 2 X 2 + 14x + 49

7. Perfect Square Trinomials Create perfect square trinomials. x 2 + 20x + ___ x 2 - 4x + ___ x 2 + 5x + ___ 100 4 25/4

8. Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation

9. Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

10. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

11. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

12. Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

13. Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation.

14. Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.

15. Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

16. Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

17. Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.