1. Factoring x2 - 9 = 0 (x + 3)(x - 3) = 0 x + 3 = 0 or x - 3 = 0
Zero-factor
property

2. Another Way to Solve Quadratics Square Root Property
Recall that we know the
solution set is
x = {-3, 3}
When you introduce the radical
you must use + and - signs.

3. 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

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

5. 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) X2 + 14x + 49

6. 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.

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

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

9. Solving Quadratic Equations by Completing the Square

10. Section 8.1
Completing the Square

11. Factoring (x + 3)(x - 5) = 0 x + 3 = 0 or x - 5 = 0 x = -3 or x = 5
Before today the only way we had for solving quadratics was to factor.
x2 - 2x - 15 = 0
(x + 3)(x - 5) = 0
x + 3 = 0 or x - 5 = 0
x = -3 or x = 5
x = {-3, 5}
Zero-factor
property

12. OR Square Root Property
If x and b are complex numbers and if x 2 = b, then OR

13. Solve each equation. Write radicals in simplified form.
Square Root Property

14. Solve each equation. Write radicals in simplified form.
Square Root Property
Radical will not simplify.

15. HW Requests: pg 303 #42-49; Pg 310 #15-37 odds
AAT-A Date: 2/5/14 SWBAT complete the square to solve factoring problems
Do Now:
HW Requests: pg 303 #42-49; Pg 310 #15-37 odds
In Class: Start Completing the Square WS
HW: Complete WS KutaSoftware 1-24 odds
Begin Section 6.5
Announcements:
Tutoring: Tues. and Thurs. 3-4
Bring Graphing Calculator to
Class for Thursday
Quiz Friday w/HW Quiz before
Complete presentations
Life Is Just A Minute Life is just a minute—only sixty seconds in it. Forced upon you—can't refuse it. Didn't seek it—didn't choose it. But it's up to you to use it. You must suffer if you lose it. Give an account if you abuse it. Just a tiny, little minute, But eternity is in it! By Dr. Benjamin Elijah Mays,
Past President of Morehouse College

16. Homework Quiz
Solve each equation by factoring. 3x2 =5x

17. Homework Quiz
Solve each equation by factoring. 3x2 =5x x= {0, 5/3}

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

19. Solve each equation. Write radicals in simplified form.
Square Root Property
Solution Set

20. Solve each equation. Write radicals in simplified form.

21. Solve each equation. Write radicals in simplified form.

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

23. 1. Divide by the coefficient of the squared term
1. Divide by the coefficient of the squared term. Make the coefficient of the squared term =1.
2. Move all variables to one side and constants to the other.
3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation.
4. Factor the left hand side and simplify the right.
5. Root and solve.
Completing the Square

24. 1. Divide by the coefficient of the squared term
1.Divide by the coefficient of the squared term. Make the coefficient of the squared term =1.
2. Move all variables to one side and constants to the other.
3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation.
4. Factor the left hand side and simplify the right.
5. Root and solve.
Completing the Square

25. Completing the Square 1. Make the coefficient of the squared term =1.
2. Move all variables to one side and constants to the other.
3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation.
4. Factor the left hand side and simplify the right.
5. Root and solve.
Completing the Square

26. 1. Divide by the coefficient of the squared term
1.Divide by the coefficient of the squared term. Make the coefficient of the squared term =1.
2. Move all variables to one side and constants to the other.
3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation.
4. Factor the left hand side and simplify the right.
5. Root and solve.
Completing the Square

27. 1. Make the coefficient of the squared term =1.
2. Move all variables to one side and constants to the other.
3. Take half of the coefficient of the x term and square it. Then add to both sides of the equation.
4. Factor the left hand side and simplify the right.
5. Root and solve.

28. Solving Quadratic Equations by Completing the Square
x2 - 2x - 15 = 0
(x + 3)(x - 5) = 0
x + 3 = 0
or x - 5 = 0
x = -3 or x = 5
x = {-3, 5}
Now take
1/2 of the coefficient of x.
Square it.
Add the result to both sides.
Factor the left.
Simplify the right.
Square Root Property

29. 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.

30. Deriving The Quadratic Formula
Divide both sides by a
Complete the square by adding (b/2a)2 to both sides
Factor (left) and find LCD (right)
Combine fractions and take the square root of both sides
Subtract b/2a and simplify

31. 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.

32. 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.

33. 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.

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