2x(3x-1)=0 eching

$$2x(3x-1)=0$$

x uchun yechish

$$x=\frac{1}{3}\approx 0,333333333$$

$$x=0$$

Faktorlash qadamlari

2x ga 3x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x omili.

$$x\left(6x-2\right)=0$$

Tenglamani yechish uchun x=0 va 6x-2=0 ni yeching.

$$x=0 x=\frac{1}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga 3x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

\left(-2\right)^{2} ning kvadrat ildizini chiqarish.

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

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{2±2}{12}$$

x=\frac{2±2}{12} tenglamasini yeching, bunda ± musbat. 2 ni 2 ga qo'shish.

$$x=\frac{4}{12}$$

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

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

x=\frac{2±2}{12} tenglamasini yeching, bunda ± manfiy. 2 dan 2 ni ayirish.

$$x=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{1}{3} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

2x ga 3x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-2x}{6}=\frac{0}{6}$$

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

$$x^{2}+\left(-\frac{2}{6}\right)x=\frac{0}{6}$$

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

$$x^{2}-\frac{1}{3}x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x^{2}-\frac{1}{3}x=0$$

-\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.

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

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

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

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

$$x=\frac{1}{3} x=0$$