1. 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. x 2 – 6x + 7 = 0b. p 2 + 2p + 1 = 0c. k 2 – 4k + 9 = 0 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. (p + 1) 2 = 0 |p + 1| = 0 p + 1 = 0 p = -1

2. 5.2.3 MORE COMPLETING THE SQUARE January 27, 2016

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 x 2 + 5x + 2 = 0 in perfect square form. First, she rewrites the equation as x 2 + 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 x 2 + 5x, as shown below. a. How many unit tiles are missing from Jessica’s square? 6.25 b. Help Jessica finish her problem by writing the perfect square form of her equation. (x + 2.5) 2 = 4.25

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 x 2 – 6x + 7 = 0 to (x – 3) 2 = 2. a. 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. b. 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 x 2 + 10x – 3 = 0 in perfect square form, what will the dimensions of the square be? x + 5 Add 25 to each side

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. w 2 + 28w + 52 = 0b. x 2 + 5x + 4 = 0 c. k 2 − 16k = 17 d. x 2 − 24x + 129 = 0 w 2 + 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