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Warm Up for Section 3.3 Factor: (1). x2 – 49 (2). x2 + 6x – 16 (3). a2 – 7a + 12 (4). 6x2 + x – 15 (5). 3xa – 2xc + 6ay – 4yc Answers for Warm Up for Section 3.3 Factor: (1). x2 – 49 = (x + 7) (x – 7) (2). x2 + 6x – 16 = (x + 8 )(x – 2) (3). a2 – 7a + 12 = (a – 3)(a – 4) (4). 6x2 + x – 15 = (3x + 5)(2x – 3) (5). 3xa – 2xc + 6ay – 4yc = (x + 2y)(3a – 2c) Solving Quadratic Equations by Taking Square Roots Section 3.3 Essential Question: How do I solve quadratic equations by using square roots? Rules for solving by taking the square root: 1) Isolate the squared variable. 2) Take the square root of both sides. 3) Do not forget that you will usually have 2 answers! Solve the equation by taking square roots: (1). x2 – 5 = 0 x2 = 5 Add 5 to both sides x= 5 Take square root of each side Solution set: 5 Solve the equation by taking square roots: (2). 2x2 – 3 = 93 2x2 = 96 Add 3 to both sides x2 = 48 Divide both sides by 2 x = 48 Take square root of each side x = 4 3 Simplify radical Solution set: 4 3 Solve the equation by taking square roots: (3). ½(y – 2)2 + 1 = 4 ½(y – 2)2 = 3 (y – 2)2 = 6 (y – 2) = 6 y = 2 6 Solution set: 2 6 Subtract 1 from both sides Multiply both sides by 2 Take square root of each side Add 2 to both side Solve the equation by taking square roots: (4). 2(y2 – 5) = -y2 – 1 2y2 – 10 = -y2 – 1 3y2 – 10 = – 1 3y2 = 9 Distribute Add y2 to both sides Add 10 to both sides y2 = 3 Divide both sides by 3 y= 3 Take square root of both sides Solution set: 3 Try these with your partner: (5). x2 – 19 = 0 (7). 3(x – 19 5)2 (6). 5(x – 4)2 = 125 = 21 5 7 (9). 3(x – 3)2 + 2 = 26 3 2 2 1, 9 (8). 3 2 x 2 5 5 5 10. The edge of a cube has the measure of (x + 5) units. The surface area of the cube is 864 square units. What is the measure of the edge of the cube? 6(x + 5)2 = SA 6(x + 5) 2 = 864 (x + 5) 2 = 144 x + 5 = ± 12 x = -5 ± 12 x = -17, 7 Edge = x + 5 = 7 + 5 = 12 12 units