Completing the Square

1. Completing the Square • This is an x. Show mex2. x x2 Show me x2 + 6x

2. Completing the Square x x x x x x x2 x2 Let's Make a Square

3. Completing the Square How many units are required to complete the square? 9! The picture is now x2 + 6x + 9, which factors (x+3)(x+3) = (x+3)2

4. Let’s Try Another One! • Show me x2 + 2x Let's Make a Square x x x2

5. Completing the Square How many units are required to complete the square? 1! x2 x2 The picture is now x2 + 2x + 1 which factors (x+1)(x+1) = (x+1)2

6. Last One with Manipulatives Show me x2 + 8x Let's Make a Square x x x x x x x x x2

7. Completing the Square Again, how many units are required to complete the square? 16 So,the picture is now x2 + 8x + 16 which factors (x+4)(x+4) = (x+4)2

8. Hard One! Complete the square for x2 + 18x + ___ How many units are needed? There are not enough pieces to do this problem. Can we do it using paper and pencil?

9. Perfect Square Trinomials • Examples • x2 + 6x + 9 • x2 - 10x + 25 • x2 + 12x + 36

10. Creating a Perfect Square Trinomial • In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ • Find the constant term by squaring half the coefficient of the linear term. • (14/2)2 X2 + 14x + 49

11. Perfect Square Trinomials • Create perfect square trinomials. • x2 + 20x + ___ • x2 - 4x + ___ • x2 + 5x + ___ 100 4 25/4

12. 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

13. 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.

14. 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.

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

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

17. 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.

18. 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.

19. 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.

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

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

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