3x(x+6)=0 eching

$$3 x ( x + 6 ) = 0$$

x uchun yechish

$$x=-6$$

$$x=0$$

Faktorlash qadamlari

3x ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+18x=0$$

x omili.

$$x\left(3x+18\right)=0$$

Tenglamani yechish uchun x=0 va 3x+18=0 ni yeching.

$$x=0 x=-6$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+18x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 18 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-18±\sqrt{18^{2}}}{2\times 3}$$

18^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-18±18}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-18±18}{6}$$

x=\frac{-18±18}{6} tenglamasini yeching, bunda ± musbat. -18 ni 18 ga qo'shish.

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

0 ni 6 ga bo'lish.

$$x=0$$

x=\frac{-18±18}{6} tenglamasini yeching, bunda ± manfiy. -18 dan 18 ni ayirish.

$$x=-\frac{36}{6}$$

-36 ni 6 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=0 x=-6$$

Kvadratni yakunlash bo'yicha qadamlar

3x ga x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+18x=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}+18x}{3}=\frac{0}{3}$$

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

$$x^{2}+\frac{18}{3}x=\frac{0}{3}$$

18 ni 3 ga bo'lish.

$$x^{2}+6x=\frac{0}{3}$$

0 ni 3 ga bo'lish.

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

6 ni bo‘lish, x shartining koeffitsienti, 2 ga 3 olish uchun. Keyin, 3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+6x+3^{2}=3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=9$$

x^{2}+6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+3\right)^{2}=9$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{9}$$

Qisqartirish.

$$x+3=3 x+3=-3$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=0 x=-6$$