5-71. Solve the two equations below. Be ready to share your method(s) with the class. a. x 2 + 4x + 1 = 0b. (x + 2) 2 = 3.

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5-71. Solve the two equations below. Be ready to share your method(s) with the class. a. x 2 + 4x + 1 = 0b. (x + 2) 2 = 3

5.2.2 Completing the Square January 26, 2016

Objectives CO: SWBAT rewrite a quadratic into the form (x – p) 2 = q by completing the square. LO: SWBAT explain how to complete the square.

5-72. With your team, and then with the class, discuss the following questions. a.Examine the solutions to x 2 + 4x + 1 = 0 and (x + 2) 2 = 3. What do you notice? What do your observations tell you about the two equations? Justify your conclusion. They appear to be the same. b.Compare the solution methods you used in problem What are the advantages and disadvantages of each method?

5-73. COMPLETING THE SQUARE With your team, examine how the two different equations from problem 5-71 can be represented using algebra tiles as shown below. Then answer questions in parts (a) and (b). a.What can be done to the equation x 2 + 4x + 1 = 0 that will result in the equation (x + 2) 2 = 3? Add 3 to both sides. b.Changing a quadratic equation into perfect square form is also known as completing the square. Why is this name appropriate?

5-74. Use what you learned in problem 5-73 to rewrite the quadratic equations below in perfect square form. Then solve the resulting quadratic equations. Record your work. Write your answers in both exact and approximate forms.

5-75. Use algebra tiles to help rewrite each equation below in perfect square form. Then solve the resulting quadratic equation. Record your work. Write your answers in both exact and approximate forms. a.x 2 + 4x – 5 = 0 x 2 + 4x = 5 x 2 + 4x + 4 = x 2 + 4x + 4 = 9 (x + 2) 2 = 9 |x + 2| = 3 x + 2 = 3 or x + 2 = -3 x = 1 or x = -5