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messersmith_power_intermediate_algebra_1e_ch4_7_10

Here are the steps to use to solve a quadratic equation by factoring: Procedure Solving a Quadratic Equation by Factoring 1) Write the equation in the form ax2 bx c 0 (standard form) so that all terms are on one side of the equal sign and zero is on the other side. 2) Factor the expression. 3) Set each factor equal to zero, and solve for the variable. (Use the zero product rule.) 4) Check the answer(s). YOU TRY 2 Solve h2 9h 18 0. EXAMPLE 3 Solve each equation by factoring. a) 2r2 3r 20 b) 6d2 42d c) k2 12(k 3) d) 2(x2 5) 5x 6x(x 1) 16 e) (z 8)(z 4) 5 Solution a) Begin by writing 2r2 3r 20 in standard form, ar2 br c 0. 2r2 3r 20 0 Standard form (2r 5)(r 4) 0 Factor. b R 2r 5 0 or r 4 0 Set each factor equal to zero. 2r 5 r 5 2 or r 4 Solve. Check in the original equation: If r 5 2 , If r 4, 2(4)2 3(4) 20 2(16) 12 20 32 12 20 ✓ 2 a5 2 b 2 3 a5 2 b 20 2 a25 4 b 15 2 20 25 2 15 2 20 40 2 20 ✓ The solution set is e4, 5 2 f . b) Write 6d2 42d in standard form. 6d 2 42d 0 Standard form 6d(d 7) 0 Factor. b R 6d 0 or d 7 0 Set each factor equal to zero. d 0 or d 7 Solve. Check. The solution set is 57, 06. Are you writing out the steps as you read the example? www.mhhe.com/messersmith SECTION 7.4 Solving Quadratic Equations by Factoring 395


messersmith_power_intermediate_algebra_1e_ch4_7_10
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