1. 5-83. Solve each quadratic equation below by completing the square
5-83. Solve each quadratic equation below by completing the square.  You may use algebra tiles or draw a diagram to represent the tiles.  Write your answers in exact form.  Then explain how you can determine how many solutions a quadratic equation has once it is written in perfect square form.
a. x2 – 6x + 7 = 0
b. p2 + 2p + 1 = 0
c. k2 – 4k + 9 = 0
k2 – 4k  = -9
k2 – 4x + 4 = -5
(k – 2)2 = -5
|k – 2| = −5
No Real Solution
x2 – 6x = -7 x2 – 6x + 9 = 2 (x – 3)2 = 2 |x – 3| = 2 x – 3 = 2 or x – 3 = - 2 x = or 3 – 2
(p + 1)2 = 0
|p + 1| = 0
p + 1 = 0
p = -1
Warm Up
5-84. Instead of using algebra tiles, how can you use an area model to complete the square for each equation in problem 5-83?  Show your work clearly.

2. 5.2.3 More Completing the Square
January 24, 2019
HW: 5-89 through 5-94

3. Objectives
CO: SWBAT solve quadratic equations by first rewriting the quadratic in perfect square form.
LO: SWBAT generalize the process of completing the square.

4. 5-85. Jessica wants to complete the square to rewrite x2 + 5x + 2 = 0 in perfect square form.  First, she rewrites the equation as x2 + 5x = –2.  But how can she split the five x-tiles into two equal parts? Jessica decides to use force!  She cuts one x-tile in half and starts to build a square from the tiles representing x2 + 5x, as shown below.
How many unit tiles are missing from Jessica’s square?
6.25
Help Jessica finish her problem by writing the perfect square form of her equation.
(x + 2.5)2 = 4.25
TEAM: I-Spy if needed

5. 5-86. Examine your work in problems 5-84 and 5-85 and compare the standard form of each equation to the corresponding equation in perfect square form.  For example, compare x2 – 6x + 7 = 0 to (x – 3)2 = 2.  
What patterns can you identify that are true for every pair of equations?
The number in the parenthesis is always half of the x-term. The number added to each side is square the number that is halved.
When a quadratic equation in standard form is changed to perfect square form, how can you predict what will be in the parentheses?  For example, if you want to rewrite x2 + 10x – 3 = 0 in perfect square form, what will the dimensions of the square be? What number would complete the square?
x + 5
Add 25 to each side
Swapmeet

6. 5-87. Use the patterns you found in problem 5-86 to help you rewrite each equation below in perfect square form and then solve it.
a. w2 + 28w + 52 = 0
b. x2 + 5x + 4 = 0
c. k2 − 16k  = 17  
d. x2 − 24x + 129 = 0
x2 + 5x  = - 4
(x + 2.5)2 = 2.25
|x + 2.5| =
x = or x = -1.5
x = or x = -4
x2 – 24x  = -129
(x – 12)2 = 15
|x – 12| = 15
x – 12 = or x – 12 =
x = or 12 – 15
x ≈ or 8.13
w2 + 28w = - 52 (w + 14)2 = 144 |w + 14| = 12 w + 14 = 12 or w + 14 = -12 w = -2 or w = -26 (k – 8)2 = 81 |k – 8| = 9 k – 8 = 9 or k – 8 = -9 k = 17 or k = -1
Pairs Check