3x(x-1)=2-2x eching

$$3 x ( x - 1 ) = 2 - 2 x$$

x uchun yechish

$$x=-\frac{2}{3}\approx -0,666666667$$

$$x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-3x=2-2x$$

Ikkala tarafdan 2 ni ayirish.

$$3x^{2}-3x-2=-2x$$

2x ni ikki tarafga qo’shing.

$$3x^{2}-3x-2+2x=0$$

-x ni olish uchun -3x va 2x ni birlashtirish.

$$3x^{2}-x-2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -1 ni b va -2 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 3\left(-2\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-12\left(-2\right)}}{2\times 3}$$

-12 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+24}}{2\times 3}$$

1 ni 24 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{25}}{2\times 3}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±5}{2\times 3}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±5}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{1±5}{6}$$

x=\frac{1±5}{6} tenglamasini yeching, bunda ± musbat. 1 ni 5 ga qo'shish.

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

6 ni 6 ga bo'lish.

$$x=1$$

x=\frac{1±5}{6} tenglamasini yeching, bunda ± manfiy. 1 dan 5 ni ayirish.

$$x=-\frac{4}{6}$$

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

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

3x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-3x=2-2x$$

2x ni ikki tarafga qo’shing.

$$3x^{2}-3x+2x=2$$

-x ni olish uchun -3x va 2x ni birlashtirish.

$$3x^{2}-x=2$$

Ikki tarafini 3 ga bo‘ling.

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

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

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

-\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{6} olish uchun. Keyin, -\frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{3}x+\left(-\frac{1}{6}\right)^{2}=\frac{2}{3}+\left(-\frac{1}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{6} kvadratini chiqarish.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{2}{3}+\frac{1}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2}{3} ni \frac{1}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{25}{36}$$

x^{2}-\frac{1}{3}x+\frac{1}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{25}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{25}{36}}$$

Qisqartirish.

$$x-\frac{1}{6}=\frac{5}{6} x-\frac{1}{6}=-\frac{5}{6}$$

\frac{1}{6} ni tenglamaning ikkala tarafiga qo'shish.

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