1. 9-5 Completing the square
Mini QUIZ 9.4 today!
Warm up
Factor
Write in standard form
Solve

2. Solve by completing the square
Activity
HW – Worksheet & Delta Math 55%!!!
Mini Quiz 9.5
Solve by completing the square
6 Steps
Keep and on same side of equation.
Move # to other side of equation.
Add to BOTH SIDES of the equation.
Factor left, Simplify Right
Square root BOTH SIDES of equation.
Solve.

3. Example 1: Do Steps 1-3 Only

4. Example 2: Do Steps 1-3 Only

5. Go back to example 1 (do steps 4-5 only)

6. Go back to example 2 (do steps 4-5 only)

7. Go back to Example 1 (Final step 6)

8. Go back to Example 2 (Final step 6)

9. Example 3: SOLVE (by completing the square)

10. Continued…

11. Example 4: SOLVE (by completing the square)

12. Continued…

13. Continued…

14. Homework
You can TRY the 3rd assignment.. More practice tomorrow!

17. x2 + 12x + ____ = x • 2 • ____ = 12x 9x2 – 42x + ____ =
COMPLETE THE SQUARE
x2 + 12x + ____ =
x • 2 • ____ = 12x
9x2 – 42x + ____ =
3x • 2 • ____ = 42x
x2 + 7x + ____ =
x • 2 • ____ = 7x 36
(x + 6)2 6 49
(3x – 7)2 7
49/4
(x + 7/2)2
7/2

18. x2 – 20x + ____ = 16y2 + 8y + ____ = x2 + 5x + ____ = 100 (x – 10)2 1
TOO
x2 – 20x + ____ =
16y2 + 8y + ____ =
x2 + 5x + ____ =
100
(x – 10)2 1
(4y + 1)2
25/4
(x + 5/2)2

19. Example 1 m2 + 4m – 9 = 0 + 9 +9 m2 + 4m + _____ = 9 + ____
m2 + 4m + _____ = 9 + ____
m • 2 • _____ = 4m
(m + 2)2 = 13
m + 2 = ±√13
m = -2 ±√13
Round to the nearest hundredth (2 #’s after the decimal) 4 4 2

20. Solving by Completing the Square:
Move constant to other side
Put in two blank spaces
Complete Square
Add the same # to both sides
Write (x ± #)2 = value
Square root both sides – Don’t forget ±
Solve – 2 answers

21. Example 2 x2 – 8x + 15 = 0 - 15 -15 x2 – 8x + _____ = -15 + ____
x2 – 8x + _____ = ____
x • 2 • _____ = 8x
(x – 4)2 = 1
x – 4 = ±1
x = 4 ± 1 16 16 4

22. TOO x2 – 12x + 35 = 0 n2 + 16n + 10 = -4 Answers: x = 5, 7