標題:
F.4 MATH quadratic equation!
發問:
5x(x-3)+4(x+4)=31-7x^2 答案係5/3 or -3/4 我聽日就考math 勁人唔該幫我解下~~
最佳解答:
5x(x-3)+4(x+4)=31-7x^2 ...... (*) Our target is to convert (*) into the form of ax^2 + bx + c = 0. 5x(x-3)+4(x+4)=31-7x^2 5x^2 - 15x + 4x + 16 = 31 - 7x^2 12x^2 - 11x - 15 = 0 Then solve it by either factorization, completing square or using quadratic formula... or calculator... Factorization: 12x^2 - 11x - 15 = 0 (3x - 5)(4x + 3) = 0 x = 5/3 or -4/3 Completing Square: 12x^2 - 11x - 15 = 0 12(x^2 - 11x/12) = 15 12[x^2 - 11x / 12 + (11/24)^2 - (11/24)^2] = 15 12(x - 11/24)^2 - 12(121/576) = 15 12(x - 11/24)^2 = 15 + 121 / 48 = 841/48 (x - 11/24)^2 = 841 / 576 x - 11/24 = √(841 / 576) = 29/24 x = (11+29)/24 or (11-29)/24 = 5/3 or -4/3 Quadratic Formula: 12x^2 - 11x - 15 = 0 x = {-(-11)√[(-11)^2 - 4(12)(-15)]} / 2(12) = (11 √841) / 24 = (11+29)/24 or (11-29)/24 = 5/3 or -4/3 Good Luck for Your Maths Exam!
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5x(x-3)+4(x+4)=31-7x^2 5x^2-15x+4x+16=31-7x^2 12x^2-11x-15=0 (4x+3)(3x-5)=0 x=-3/4 or 5/3
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