Warm-up

1. What are the different ways to solve quadratic equation?

Solve the following problem by completing the square.

22. 10 16x x

Objective - To solve quadratic equations by completing the square.

Methods for Solving Quadratic Equations1) Square Root Method (Doesn’t work with

linear terms)

x2 92) Graphic Method

y x2 2x 3(Often difficult to tell)

x=-1 x=3

3) Quadratic Formula

0 x2 2x 3a=1b= -2c= -3

x b b2 4ac

2a

(Always works)

4) Factoring Method

0 (x 1)(x 3)(Works when factorable)

5) Completing the Square (Always works)

2

Solve by completing the square.

x2 5x 6 0

6 6

x2 5x 6

Complete the square

254

52

254

254

x2 5x 254

244

254

x 52

2

14

x 52

1

4

x 52

12

x 52

12

52

12

52

12

3

,2

#1

2

Solve by completing the square.

x2 7x 0

x2 7x 0

Complete the square

494

72

494

494

x2 7x 494

494

x 72

2

494

x 72

49

4

x 72

72

x 72

72

72

72

72

72

7

,0

#2

2

x2 72

x 2

Solve by completing the square.

2x2 7x 4 0

4 4

4916

12

72

4916

4916

x 74

2

8116

x 74

81

16

x 74

94

x 74

94

74

94

74

94

2x2 7x 4

2 2

x 74

2

3216

4916

74

2

74

74

24

164

12

, 4

#3

2

x2 53

x 13

Solve by completing the square.

3x2 5x 1 0

1 1

2536

12

53

2536

2536

x 56

2

1336

x 56

13

36

x 56

136

x 56

136

3x2 5x 1

3 3

x 56

2

1236

2536

56

2

56

56

x 5 13

6

#4

Practice21. 3 0x x

Practice22. 3 6 2 0x x

Practice23. 3 4 1 0x x

Practice24. 4 4 11 0x x

Complete the square using your white board.26 24 41 0x x