6x(x-1)=0 eching

$$6 x ( x - 1 ) = 0$$

x uchun yechish

$$x=1$$

$$x=0$$

Faktorlash qadamlari

6x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x omili.

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

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

$$x=0 x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

6x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±6}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{6±6}{12}$$

x=\frac{6±6}{12} tenglamasini yeching, bunda ± musbat. 6 ni 6 ga qo'shish.

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

12 ni 12 ga bo'lish.

$$x=1$$

x=\frac{6±6}{12} tenglamasini yeching, bunda ± manfiy. 6 dan 6 ni ayirish.

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

0 ni 12 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=1 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

6x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikki tarafini 6 ga bo‘ling.

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

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

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

-6 ni 6 ga bo'lish.

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

0 ni 6 ga bo'lish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$x^{2}-x+\frac{1}{4}=\frac{1}{4}$$

x^{2}-x+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=1 x=0$$