(-x)(3x+1)=0 eching

$$( - x ) ( 3 x + 1 ) = 0$$

x uchun yechish

$$x=-\frac{1}{3}\approx -0,333333333$$

$$x=0$$

Faktorlash qadamlari

-x ga 3x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-3 hosil qilish uchun 3 va -1 ni ko'paytirish.

$$-3xx-x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

x omili.

$$x\left(-3x-1\right)=0$$

Tenglamani yechish uchun x=0 va -3x-1=0 ni yeching.

$$x=0 x=-\frac{1}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

-x ga 3x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-3 hosil qilish uchun 3 va -1 ni ko'paytirish.

$$-3xx-x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -3 ni a, -1 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\left(-3\right)}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-1\right)±1}{2\left(-3\right)}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±1}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{1±1}{-6}$$

x=\frac{1±1}{-6} tenglamasini yeching, bunda ± musbat. 1 ni 1 ga qo'shish.

$$x=\frac{2}{-6}$$

\frac{2}{-6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{3}$$

x=\frac{1±1}{-6} tenglamasini yeching, bunda ± manfiy. 1 dan 1 ni ayirish.

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

0 ni -6 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-\frac{1}{3} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

-x ga 3x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

-3 hosil qilish uchun 3 va -1 ni ko'paytirish.

$$-3xx-x=0$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

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

Ikki tarafini -3 ga bo‘ling.

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

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

$$x^{2}+\left(-\frac{1}{-3}\right)x=\frac{0}{-3}$$

-1 ni -3 ga bo'lish.

$$x^{2}+\frac{1}{3}x=\frac{0}{-3}$$

0 ni -3 ga bo'lish.

$$x^{2}+\frac{1}{3}x=0$$

\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{1}{6} olish uchun. Keyin, \frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{1}{3}x+\left(\frac{1}{6}\right)^{2}=\left(\frac{1}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{1}{6} kvadratini chiqarish.

$$x^{2}+\frac{1}{3}x+\frac{1}{36}=\frac{1}{36}$$

x^{2}+\frac{1}{3}x+\frac{1}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{1}{6}\right)^{2}=\frac{1}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{1}{6}\right)^{2}}=\sqrt{\frac{1}{36}}$$

Qisqartirish.

$$x+\frac{1}{6}=\frac{1}{6} x+\frac{1}{6}=-\frac{1}{6}$$

Tenglamaning ikkala tarafidan \frac{1}{6} ni ayirish.

$$x=0 x=-\frac{1}{3}$$