5x(x-7)=0 eching

$$5 x ( x - 7 ) = 0$$

x uchun yechish

$$x=7$$

$$x=0$$

Faktorlash qadamlari

5x ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5x^{2}-35x=0$$

x omili.

$$x\left(5x-35\right)=0$$

Tenglamani yechish uchun x=0 va 5x-35=0 ni yeching.

$$x=0 x=7$$

Kvadrat tenglamalaridan foydalanish qoidalari

5x ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5x^{2}-35x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -35 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-35\right)±\sqrt{\left(-35\right)^{2}}}{2\times 5}$$

\left(-35\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-35\right)±35}{2\times 5}$$

-35 ning teskarisi 35 ga teng.

$$x=\frac{35±35}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{35±35}{10}$$

x=\frac{35±35}{10} tenglamasini yeching, bunda ± musbat. 35 ni 35 ga qo'shish.

$$x=\frac{70}{10}$$

70 ni 10 ga bo'lish.

$$x=7$$

x=\frac{35±35}{10} tenglamasini yeching, bunda ± manfiy. 35 dan 35 ni ayirish.

$$x=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=7 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

5x ga x-7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$5x^{2}-35x=0$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-35x}{5}=\frac{0}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{35}{5}\right)x=\frac{0}{5}$$

-35 ni 5 ga bo'lish.

$$x^{2}-7x=\frac{0}{5}$$

0 ni 5 ga bo'lish.

$$x^{2}-7x=0$$

-7 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{2} olish uchun. Keyin, -\frac{7}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{2} kvadratini chiqarish.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

x^{2}-7x+\frac{49}{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.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Qisqartirish.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

\frac{7}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=7 x=0$$