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messersmith_power_introductory_algebra_1e_ch4_7_10

Solve using the square root property. a) x2 4 b) c2 45 0 c) 2n2 7 19 d) y2 15 6 Solution a) x2 4 b R x 14 or x 14 Square root property x 2 or x 2 Check: x 2: x2 4 x 2: x2 4 (2)2 4 (2)2 4 4 4 ✓ 4 4 ✓ The solution set is {2, 2}. We can also write it as {2}. An equivalent way to solve x2 4 is to write it as x2 4 x 14 Square root property x 2 We will use this approach when solving equations using the square root property. b) To solve c2 45 0, begin by getting c2 on a side by itself. c2 45 0 c2 45 Add 45 to each side. c 145 Square root property c 19 15 Product rule for radicals c 315 19 3 The check is left to the student. The solution set is {315, 315} or {315}. c) To solve 2n2 7 19, begin by getting 2n2 on a side by itself. 2n2 7 19 2n2 12 Subtract 7 from each side. n2 6 Divide by 2. n 16 Square root property The check is left to the student. The solution set is {16, 16} or {16}. d) y2 15 6 y2 9 Subtract 15 from each side. y 19 Square root property Since 19 is not a real number, there is no real number solution to y2 15 6. The solution set is . EXAMPLE 1 In-Class Example 1 Solve using the square root property. a) g2 36 b) t2 60 0 c) 4r2 25 1 d) h2 33 9 Answer: a) {6, 6} b) {2115, 2115} c) e 126 2 , 126 2 f d) Remember to write out the steps in the example as you are reading it. YOU TRY 1 Solve using the square root property. a) m2 25 b) h2 28 0 c) 4a2 9 49 d) p2 30 14 www.mhhe.com/messersmith SECTION 10.1 Solving Quadratic Equations Using the Square Root Property 607


messersmith_power_introductory_algebra_1e_ch4_7_10
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