2x(3x-2)-4=x eching

$$2x(3x-2)-4=x$$

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1,333333333$$

Guruhlash orqali faktorlash qadamlari

2x ga 3x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-4x-4=x$$

Ikkala tarafdan x ni ayirish.

$$6x^{2}-4x-4-x=0$$

-5x ni olish uchun -4x va -x ni birlashtirish.

$$6x^{2}-5x-4=0$$

Tenglamani yechish uchun guruhlash orqali chap qoʻl tomonni faktorlang. Avvalo, chap qoʻl tomon 6x^{2}+ax+bx-4 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-5 ab=6\left(-4\right)=-24$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -24-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-24 2,-12 3,-8 4,-6$$

Har bir juftlik yigʻindisini hisoblang.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

Yechim – -5 yigʻindisini beruvchi juftlik.

$$a=-8 b=3$$

6x^{2}-5x-4 ni \left(6x^{2}-8x\right)+\left(3x-4\right) sifatida qaytadan yozish.

$$\left(6x^{2}-8x\right)+\left(3x-4\right)$$

6x^{2}-8x ichida 2x ni ajrating.

$$2x\left(3x-4\right)+3x-4$$

Distributiv funktsiyasidan foydalangan holda 3x-4 umumiy terminini chiqaring.

$$\left(3x-4\right)\left(2x+1\right)$$

Tenglamani yechish uchun 3x-4=0 va 2x+1=0 ni yeching.

$$x=\frac{4}{3} x=-\frac{1}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga 3x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-4x-4=x$$

Ikkala tarafdan x ni ayirish.

$$6x^{2}-4x-4-x=0$$

-5x ni olish uchun -4x va -x ni birlashtirish.

$$6x^{2}-5x-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -5 ni b va -4 ni c bilan almashtiring.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 6\left(-4\right)}}{2\times 6}$$

-5 kvadratini chiqarish.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 6\left(-4\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25-24\left(-4\right)}}{2\times 6}$$

-24 ni -4 marotabaga ko'paytirish.

$$x=\frac{-\left(-5\right)±\sqrt{25+96}}{2\times 6}$$

25 ni 96 ga qo'shish.

$$x=\frac{-\left(-5\right)±\sqrt{121}}{2\times 6}$$

121 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-5\right)±11}{2\times 6}$$

-5 ning teskarisi 5 ga teng.

$$x=\frac{5±11}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{5±11}{12}$$

x=\frac{5±11}{12} tenglamasini yeching, bunda ± musbat. 5 ni 11 ga qo'shish.

$$x=\frac{16}{12}$$

\frac{16}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{4}{3}$$

x=\frac{5±11}{12} tenglamasini yeching, bunda ± manfiy. 5 dan 11 ni ayirish.

$$x=-\frac{6}{12}$$

\frac{-6}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{4}{3} x=-\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x ga 3x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-4x-4=x$$

Ikkala tarafdan x ni ayirish.

$$6x^{2}-4x-4-x=0$$

-5x ni olish uchun -4x va -x ni birlashtirish.

$$6x^{2}-5x-4=0$$

4 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$6x^{2}-5x=4$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-5x}{6}=\frac{4}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{5}{6}x=\frac{4}{6}$$

\frac{4}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{5}{6}x=\frac{2}{3}$$

-\frac{5}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{12} olish uchun. Keyin, -\frac{5}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{5}{6}x+\left(-\frac{5}{12}\right)^{2}=\frac{2}{3}+\left(-\frac{5}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{12} kvadratini chiqarish.

$$x^{2}-\frac{5}{6}x+\frac{25}{144}=\frac{2}{3}+\frac{25}{144}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2}{3} ni \frac{25}{144} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{5}{6}x+\frac{25}{144}=\frac{121}{144}$$

x^{2}-\frac{5}{6}x+\frac{25}{144} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{5}{12}\right)^{2}=\frac{121}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{12}\right)^{2}}=\sqrt{\frac{121}{144}}$$

Qisqartirish.

$$x-\frac{5}{12}=\frac{11}{12} x-\frac{5}{12}=-\frac{11}{12}$$

\frac{5}{12} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{4}{3} x=-\frac{1}{2}$$