3x(x-5)=0 eching

$$3x(x-5)=0$$

x uchun yechish

$$x=5$$

$$x=0$$

Faktorlash qadamlari

3x ga x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-15x=0$$

x omili.

$$x\left(3x-15\right)=0$$

Tenglamani yechish uchun x=0 va 3x-15=0 ni yeching.

$$x=0 x=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-15x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -15 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}}}{2\times 3}$$

\left(-15\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-15\right)±15}{2\times 3}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±15}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{15±15}{6}$$

x=\frac{15±15}{6} tenglamasini yeching, bunda ± musbat. 15 ni 15 ga qo'shish.

$$x=\frac{30}{6}$$

30 ni 6 ga bo'lish.

$$x=5$$

x=\frac{15±15}{6} tenglamasini yeching, bunda ± manfiy. 15 dan 15 ni ayirish.

$$x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=5 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

3x ga x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-15x=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-15x}{3}=\frac{0}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{15}{3}\right)x=\frac{0}{3}$$

-15 ni 3 ga bo'lish.

$$x^{2}-5x=\frac{0}{3}$$

0 ni 3 ga bo'lish.

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

-5 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{2} olish uchun. Keyin, -\frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$x^{2}-5x+\frac{25}{4}=\frac{25}{4}$$

x^{2}-5x+\frac{25}{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.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

$$x-\frac{5}{2}=\frac{5}{2} x-\frac{5}{2}=-\frac{5}{2}$$

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=5 x=0$$