384 CHAPTER 6 Algebra, Graphs, and Functions Applications of Quadratic Equations = ± − = ± 8 64 16 8 8 48 8 Since 48 163 43 = = (see Section 5.4), we write ± = ± = ± = ± 8 48 8 8 4 3 8 4(2 3) 8 2 3 2 1 2 The solutions are 2 3 2 + and 2 3 2 . − 7 Now try Exercise 75 Note that the solutions to Example 11 are irrational numbers. 2x 1 30 2x 1 40 x x x x 40 30 Figure 6.40 Example 12 Brick Border Pablo and Maya recently installed an inground rectangular swimming pool measuring 40 ft by 30 ft. They want to add a brick border of uniform width around all sides of the pool. How wide can they make the brick border if they purchased enough brick to cover an area of 296 ft ?2 Solution Let’s make a diagram of the pool and the brick border (Fig. 6.40). Let x the = uniform width of the brick border. Then the total length of the larger rectangular area, the pool plus the border, is x2 40. + The total width of the larger rectangular area is x2 30. + The area of the brick border can be determined by subtracting the area of the pool from the area of the pool plus the brick border. = ⋅ = = = ⋅ = + + = + + = − = + + − = + l w l w x x x x x x x x Area of pool (40)(30) 1200 ft Area of pool plus brick border (2 40)(2 30) 4 140 1200 Area of the brick border area of pool plus brick border area of pool (4 140 1200) 1200 4 140 2 2 2 2 The area of the brick border must be 296 ft .2 Therefore, x x 296 4 140 2 = + or + − = + − = + − = + − = + − = x x x x x x x x x x 4 140 296 0 4( 35 74) 0 4 4 ( 35 74) 0 4 35 74 0 ( 37)( 2) 0 2 2 2 2 Factor out 4 from each term. Divide both sides of the equation by 4. Factor trinomial. x x x x 370 or 2 0 37 2 + = − = = − = Since lengths are positive, the only possible answer is x 2. = Thus, they can make a brick border 2 ft wide all around the pool. 7 Now try Exercise 81 Instructor Resources for Section 6.9 in MyLab Math • Objective-Level Videos 6.9 • PowerPoint Lecture Slides 6.9 • MyLab Exercises and Assignments 6.9
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