b) To solve x2 10x 18 0, ask yourself, “Can I factor x2 10x 18?” No. We could solve this using the quadratic formula, but completing the square is also a good method for solving this equation. Why? Completing the square is a good method for solving a quadratic equation when the coeffi cient of the squared term is 1 or 1 and when the coeffi cient of the linear term is even. We will solve x2 10x 18 0 by completing the square. Step 1: The coeffi cient of x2 is 1. Step 2: Get the variables on one side of the equal sign and the constant on the other side: x2 10x 18 1 2 Step 3: Complete the square: (10) 5 (5)2 25 Add 25 to both sides of the equation: x2 10x 25 18 25 x2 10x 25 7 Step 4: Factor: (x 5)2 7 Step 5: Solve using the square root property: (x 5)2 7 x 5 17 x 5 17 Add 5 to each side. The solution set is {5 17, 5 17}. Note Completing the square works well when the coefficient of the squared term is 1 or 1 and when the coefficient of the linear term is even because when we complete the square in Step 3, we will not obtain a fraction. (Half of an even number is an integer.) c) Ask yourself, “Can I solve 2k2 5k 9 0 by factoring?” No. Completing the square would not be a very effi cient way to solve the equation because the coeffi cient of k2 is 2, and dividing the equation by 2 would give us k2 5 2 k 9 2 0. We will solve 2k2 5k 9 0 using the quadratic formula. Identify a, b, and c: a 2 b 5 c 9 k b 2b2 4ac 2a Quadratic formula k (5) 2(5)2 4(2)(9) 2(2) Substitute a 2, b 5, and c 9. k 5 125 72 4 5 147 4 Since 147 is not a real number, there is no real number solution to 2k2 5k 9 0. The solution set is . www.mhhe.com/messersmith Putting It All Together 629
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above