10.7 Completing the Square
Homework
Any Questions?
Solve the following:
x2 + 8x + 5
This trinomial cannot be factored!
Sometimes you will run into quadratic equations that cannot be factored so you need
to use the following method: Completing the Square
Steps for Completing the Square
1. Recognize that the equation
x2 -6x + 7 = 0
cannot be factored
2. Move “c” to the other side of the equation x2 – 6x
= -7
3. Find what a new “c” would be to make the trinomial square. Use the formula
( b/2 ) 2 = new “c” (-6/2)2 = 9
4. Add your new “c” to both sides (Golden rule) x2 -6x + 9 = -7 + 9
x2 – 6x + 9 = 2
5. Factor the left side and simplify the right side (x – 3)2 = 2
6. Solve for x (do not forget the ±)
7. Simplify your answer
√(x – 3)2 = √2
x = 3 ± √2
Cool Fact of the Day
Tsunamis (tidal waves)
travel as fast as jet
planes.
4
Example 1: Solve the following using complete the square
Step 1:
x2 -4x + 2 = 0
Step 2:
x2 – 4x = -2
Step 3:
(-4/2)2 = 4
Step 4:
x2 – 4x + 4
Step 5:
(x – 2)2 = 2
Step 6:
√(x – 2)2=√ 2
Step 7:
x = 2 ± √2
= -2 + 4
Now you have learned 5 ways to solve quadratic equations, can you list
them?
1. Use square roots: only works for ax2 + c = 0
2. Graphing: works for all quadratic equations, not exact
3. Quadratic Formula: works for all quadratic equations (slow)
4. Factoring: works for most but not all (fast)
5. Complete the square: works for all quadratic equations
Person of the Day
Cool Photo of the Day
Look how much sugar!
7
Cool Photo of the Day
Look how much sugar!
8
Cool Photo of the Day
Look how much sugar!
9
Cool Photo of the Day
Look how much sugar!
10
Practice
• Solve the equation by completing the square.
Practice
• Use the most convenient method to solve the equation.
Homework
Pg. 552 5-19 odds, 29 – 43 odds
Pg. 556, 557 #1-4, 17-26, 33-40, 47-50 (due
Tuesday)