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Algebra 2 5.5 Completing the Square Name: _______________________ Essential Question: How do we solve quadratic equations by using the square root property and by completing the square? Warm Up: Factor each of the following. a. x2 + 16x + 64 b. x2 – 34x + 289 c. 4x2 – 12x + 9 Vocabulary: ________________________________ is the process of manipulating an equation so that one side of the equation contains a perfect square trinomial. To complete the square on x2 + bx, add (1/2b)2 to both sides of the equation. x2 + bx + (1/2b)2 = (x + 1/2b)2 = (x + b/2)2 Solving using the Square Root Property: a. x2 + 14x + 49 = 64 b. x2 – 4x + 4 = 13 How to complete the square: Use x2 + 2x – 8 = 0 First step, get everything without an x on the other side of the equation. Second step, find b so that we can see what 12 b is. Third step, complete the perfect square trinomial. (Remember that whatever you do to one side of the equation, you must also do to the other side) We now have a perfect square trinomial, which can be factored into a binomial square. (Remember we just found the perfect square trinomial by expanding the binomial square. By factoring we are just “un-multiplying” it.) Fourth step, factor the perfect square trinomial. Examples: 1. Find the value for c that makes x2 + 12x + c a perfect square. Then write the trinomial as a perfect square. 2. Solve by completing the square. a. x2 + 4x – 12 = 0 b. 3x2 – 2x – 1 = 0 Summarizer: Complete the square for 0 = x2 - 10x + 10. c. x2 + 4x + 11 = 0