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2x^{2}-5x-3=114
2x+1 ga x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
2x^{2}-5x-3-114=0
Ikkala tarafdan 114 ni ayirish.
2x^{2}-5x-117=0
-117 olish uchun -3 dan 114 ni ayirish.
x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-117\right)}}{2\times 2}
Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -5 ni b va -117 ni c bilan almashtiring.
x=\frac{-\left(-5\right)±\sqrt{25-4\times 2\left(-117\right)}}{2\times 2}
-5 kvadratini chiqarish.
x=\frac{-\left(-5\right)±\sqrt{25-8\left(-117\right)}}{2\times 2}
-4 ni 2 marotabaga ko'paytirish.
x=\frac{-\left(-5\right)±\sqrt{25+936}}{2\times 2}
-8 ni -117 marotabaga ko'paytirish.
x=\frac{-\left(-5\right)±\sqrt{961}}{2\times 2}
25 ni 936 ga qo'shish.
x=\frac{-\left(-5\right)±31}{2\times 2}
961 ning kvadrat ildizini chiqarish.
x=\frac{5±31}{2\times 2}
-5 ning teskarisi 5 ga teng.
x=\frac{5±31}{4}
2 ni 2 marotabaga ko'paytirish.
x=\frac{36}{4}
x=\frac{5±31}{4} tenglamasini yeching, bunda ± musbat. 5 ni 31 ga qo'shish.
x=9
36 ni 4 ga bo'lish.
x=-\frac{26}{4}
x=\frac{5±31}{4} tenglamasini yeching, bunda ± manfiy. 5 dan 31 ni ayirish.
x=-\frac{13}{2}
\frac{-26}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.
x=9 x=-\frac{13}{2}
Tenglama yechildi.
2x^{2}-5x-3=114
2x+1 ga x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.
2x^{2}-5x=114+3
3 ni ikki tarafga qo’shing.
2x^{2}-5x=117
117 olish uchun 114 va 3'ni qo'shing.
\frac{2x^{2}-5x}{2}=\frac{117}{2}
Ikki tarafini 2 ga bo‘ling.
x^{2}-\frac{5}{2}x=\frac{117}{2}
2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.
x^{2}-\frac{5}{2}x+\left(-\frac{5}{4}\right)^{2}=\frac{117}{2}+\left(-\frac{5}{4}\right)^{2}
-\frac{5}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{4} olish uchun. Keyin, -\frac{5}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.
x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{117}{2}+\frac{25}{16}
Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{4} kvadratini chiqarish.
x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{961}{16}
Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{117}{2} ni \frac{25}{16} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.
\left(x-\frac{5}{4}\right)^{2}=\frac{961}{16}
x^{2}-\frac{5}{2}x+\frac{25}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.
\sqrt{\left(x-\frac{5}{4}\right)^{2}}=\sqrt{\frac{961}{16}}
Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.
x-\frac{5}{4}=\frac{31}{4} x-\frac{5}{4}=-\frac{31}{4}
Qisqartirish.
x=9 x=-\frac{13}{2}
\frac{5}{4} ni tenglamaning ikkala tarafiga qo'shish.