(3x+1)(x-1)-3(x+3)^2=-9 eching

$$( 3 x + 1 ) ( x - 1 ) - 3 ( x + 3 ) ^ { 2 } = - 9$$

x uchun yechish

$$x=-\frac{19}{20}=-0,95$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

3x+1 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$3x^{2}-2x-1-3\left(x+3\right)^{2}=-9$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+3\right)^{2} kengaytirilishi uchun ishlating.

$$3x^{2}-2x-1-3\left(x^{2}+6x+9\right)=-9$$

-3 ga x^{2}+6x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}-2x-1-3x^{2}-18x-27=-9$$

0 ni olish uchun 3x^{2} va -3x^{2} ni birlashtirish.

$$-2x-1-18x-27=-9$$

-20x ni olish uchun -2x va -18x ni birlashtirish.

$$-20x-1-27=-9$$

-28 olish uchun -1 dan 27 ni ayirish.

$$-20x-28=-9$$

28 ni ikki tarafga qo’shing.

$$-20x=-9+28$$

19 olish uchun -9 va 28'ni qo'shing.

$$-20x=19$$

Ikki tarafini -20 ga bo‘ling.

$$x=\frac{19}{-20}$$

\frac{19}{-20} kasri manfiy belgini olib tashlash bilan -\frac{19}{20} sifatida qayta yozilishi mumkin.

$$x=-\frac{19}{20}$$