1 Decide Which Method to Use to Solve a Quadratic Equation Solve. a) p2 6p 16 b) m2 8m 13 0 c) 3t2 8t 7 0 d) (2z 7)2 6 0 Solution a) Write p2 6p 16 in standard form: p2 6p 16 0 Does p2 6p 16 factor? Yes. Solve by factoring. ( p 8)( p 2) 0 — — p 8 0 or p 2 0 Set each factor equal to 0. p 8 or p 2 Solve. The solution set is {2, 8}. b) To solve m2 8m 13 0 ask yourself, “Can I factor m2 8m 13?” No, it does not factor. We could solve this using the quadratic formula, but completing the square is also a good method for solving this equation. Why? Note Completing the square is a good method for solving a quadratic equation when the coefficient of the squared term is 1 or 1 and when the coefficient of the linear term is even. We will solve m2 8m 13 0 by completing the square. Step 1: The coeffi cient of m2 is 1. Step 2: Get the variables on one side of the equal sign and the constant on the other side. m2 8m 13 Step 3: Complete the square: 1 2 (8) 4 (4)2 16 Add 16 to both sides of the equation. m2 8m 16 13 16 m2 8m 16 3 Step 4: Factor: (m 4)2 3 Step 5: Solve using the square root property: (m 4)2 3 m 4 13 m 4 13 The solution set is 54 13, 4 136. EXAMPLE 1 Write the solutions to the equations in this example in your notes. In your own words, explain why each method is chosen to solve each equation. www.mhhe.com/messersmith Putting It All Together 633
messersmith_power_intermediate_algebra_1e_ch4_7_10
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