If a quadratic equation is not in standard form, we must write it that way. Solve using the quadratic formula. a) t2 1 4t b) 2w(w 3) 5 Solution a) Is t2 1 4t in the form ax2 bx c 0? No. Before we can apply the quadratic formula, we must write it in that form. t2 4t 1 0 Subtract 4t. Identify a, b, and c: a 1 b 4 c 1 t b 2b2 4ac 2a Quadratic formula t (4) 2(4)2 4(1)(1) 2(1) Substitute a 1, b 4, and c 1. t 4 116 4 2 Perform the operations. t 4 112 2 Simplify the radicand. t 4 213 2 Simplify the radical. t 2(2 13) 2 Factor out 2. t 2 13 Simplify. The solution set is {2 13, 2 13}. b) Is 2w(w 3) 5 in the form ax2 bx c 0? No. Distribute on the left side of the equation, then get all terms on the same side of the equal sign. 2w2 6w 5 Distribute. 2w2 6w 5 0 Add 5. Identify a, b, and c: a 2 b 6 c 5 w b 2b2 4ac 2a Quadratic formula w (6) 2(6)2 4(2)(5) 2(2) Substitute a 2, b 6, and c 5. w 6 136 40 4 Perform the operations. w 6 14 4 Simplify the radicand. Since 14 is not a real number, there is no real number solution to 2w(w 3) 5. The solution set is . EXAMPLE 2 In-Class Example 2 Solve using the quadratic formula. a) x2 6 10x b) k(3k 2) 1 Answer: a) {5 119, 5 119} b) YOU TRY 2 Solve using the quadratic formula. a) y2 4 6y b) m(5m 2) 3 624 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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