-18x(x-1)=0 eching

$$- 18 x ( x - 1 ) = 0$$

x uchun yechish

$$x=1$$

$$x=0$$

Faktorlash qadamlari

-18x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x omili.

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

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

$$x=0 x=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

-18x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

18^{2} ning kvadrat ildizini chiqarish.

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

2 ni -18 marotabaga ko'paytirish.

$$x=\frac{-18±18}{-36}$$

x=\frac{-18±18}{-36} tenglamasini yeching, bunda ± musbat. -18 ni 18 ga qo'shish.

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

0 ni -36 ga bo'lish.

$$x=0$$

x=\frac{-18±18}{-36} tenglamasini yeching, bunda ± manfiy. -18 dan 18 ni ayirish.

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

-36 ni -36 ga bo'lish.

$$x=1$$

Tenglama yechildi.

$$x=0 x=1$$

Kvadratni yakunlash bo'yicha qadamlar

-18x ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Ikki tarafini -18 ga bo‘ling.

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

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

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

18 ni -18 ga bo'lish.

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

0 ni -18 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.

$$x=1 x=0$$