2x(9x-3)=0 eching

$$2x(9x-3)=0$$

x uchun yechish

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

$$x=0$$

Faktorlash qadamlari

2x ga 9x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}-6x=0$$

x omili.

$$x\left(18x-6\right)=0$$

Tenglamani yechish uchun x=0 va 18x-6=0 ni yeching.

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

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga 9x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}-6x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 18 ni a, -6 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 18}$$

\left(-6\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±6}{2\times 18}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±6}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$x=\frac{6±6}{36}$$

x=\frac{6±6}{36} tenglamasini yeching, bunda ± musbat. 6 ni 6 ga qo'shish.

$$x=\frac{12}{36}$$

\frac{12}{36} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

x=\frac{6±6}{36} tenglamasini yeching, bunda ± manfiy. 6 dan 6 ni ayirish.

$$x=\frac{0}{36}$$

0 ni 36 ga bo'lish.

$$x=0$$

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

2x ga 9x-3 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$18x^{2}-6x=0$$

Ikki tarafini 18 ga bo‘ling.

$$\frac{18x^{2}-6x}{18}=\frac{0}{18}$$

18 ga bo'lish 18 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{6}{18}\right)x=\frac{0}{18}$$

\frac{-6}{18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{3}x=\frac{0}{18}$$

0 ni 18 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.

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