Note In future math courses, you may learn about another set of numbers called complex numbers, which allow us to find non-real number solutions to equations like the one in Example 1d). Can we solve (a 5)2 9 using the square root property? Yes. The equation has a squared quantity and a constant. 2 Solve an Equation of the Form 1ax b22 k Solve x2 9 and (a 5)2 9 using the square root property. Solution While the equation (a 5)2 9 has a binomial that is being squared, the two equations are actually in the same form. x2 9 1a 522 9 c c c c x squared constant (a 5) squared constant Solve x2 9: x2 9 x 19 Square root property x 3 The solution set is {3, 3} or {3}. We solve (a 5)2 9 in the same way with some additional steps. (a 5)2 9 a 5 19 Square root property a 5 3 This means a 5 3 or a 5 3. Solve both equations. a 5 3 or a 5 3 a 8 or a 2 Add 5 to each side. Check: a 8: (a 5)2 9 a 2: (a 5)2 9 (8 5)2 9 (2 5)2 9 32 9 (3)2 9 9 9 ✓ 9 9 ✓ The solution set is {2, 8}. EXAMPLE 2 In-Class Example 2 Solve n2 49 and (p 11)2 49 using the square root property. Answer: {7, 7} and {4, 18} Can you write a procedure for solving equations of the form (ax b)2 k? 608 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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