8x(x-9)=0 eching

$$8 x ( x - 9 ) = 0$$

x uchun yechish

$$x=9$$

$$x=0$$

Faktorlash qadamlari

8x ga x-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x^{2}-72x=0$$

x omili.

$$x\left(8x-72\right)=0$$

Tenglamani yechish uchun x=0 va 8x-72=0 ni yeching.

$$x=0 x=9$$

Kvadrat tenglamalaridan foydalanish qoidalari

8x ga x-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x^{2}-72x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, -72 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}}}{2\times 8}$$

\left(-72\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-72\right)±72}{2\times 8}$$

-72 ning teskarisi 72 ga teng.

$$x=\frac{72±72}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{72±72}{16}$$

x=\frac{72±72}{16} tenglamasini yeching, bunda ± musbat. 72 ni 72 ga qo'shish.

$$x=\frac{144}{16}$$

144 ni 16 ga bo'lish.

$$x=9$$

x=\frac{72±72}{16} tenglamasini yeching, bunda ± manfiy. 72 dan 72 ni ayirish.

$$x=\frac{0}{16}$$

0 ni 16 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=9 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

8x ga x-9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$8x^{2}-72x=0$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8x^{2}-72x}{8}=\frac{0}{8}$$

8 ga bo'lish 8 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{72}{8}\right)x=\frac{0}{8}$$

-72 ni 8 ga bo'lish.

$$x^{2}-9x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x^{2}-9x=0$$

-9 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{2} olish uchun. Keyin, -\frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=\left(-\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.

$$x^{2}-9x+\frac{81}{4}=\frac{81}{4}$$

x^{2}-9x+\frac{81}{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.

$$\left(x-\frac{9}{2}\right)^{2}=\frac{81}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Qisqartirish.

$$x-\frac{9}{2}=\frac{9}{2} x-\frac{9}{2}=-\frac{9}{2}$$

\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=9 x=0$$