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Solving Quadratics using Bust the “b” ax2 + bx + c = 0 STEPS: 1. Factor out the GCF if necessary. 2. Make sure that a is positive. (if not divide through by –1) 3. Open two parenthesis with ax (ax )(ax ) *you now have a “fudge (extra) factor” of a 4. Multiply the first and the last numbers. Find factors of ac that combine to = b. 5. Look inside each parenthesis for GCFs 6. Solve NOTE: If Bust the “b” fails to yield solutions, there are no rational roots you must complete the square or use the quadratic formula. Example: 2x2 + 7x – 15 =0 (2x )(2x ) *fudge = 2 2*15 = 30 1 30 2 15 3 10 5 6 (2x + 10)(2x – 3) =0 2(x + 5)(2x – 3) =0 x + 5 = 0 or 2x - 3 = 0 x = -5 or x = 3/2 Example: 6x2 - 19x + 10 (6x )(6x )=0 *fudge = 6 6*10 = 60 1 2 3 4 5 6 (6x - 4)(6x – 15) = 0 2(3x - 2)3(2x – 5) = 0 x= 2 5 , x= 2 3 Try: 4x2 – 4x –15 = 0 Try: 10x2 – 34x + 12 = 0 Try: 3a4 + a2 = 18 60 30 20 15 12 10