2*(x+4)-3*(x+1)^2=x*(6-3x) eching

$$2 \cdot ( x + 4 ) - 3 \cdot ( x + 1 ) ^ { 2 } = x \cdot ( 6 - 3 x )$$

x uchun yechish

$$x=\frac{1}{2}=0,5$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2 ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x+8-3\left(x+1\right)^{2}=x\left(6-3x\right)$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$2x+8-3\left(x^{2}+2x+1\right)=x\left(6-3x\right)$$

-3 ga x^{2}+2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x+8-3x^{2}-6x-3=x\left(6-3x\right)$$

-4x ni olish uchun 2x va -6x ni birlashtirish.

$$-4x+8-3x^{2}-3=x\left(6-3x\right)$$

5 olish uchun 8 dan 3 ni ayirish.

$$-4x+5-3x^{2}=x\left(6-3x\right)$$

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

$$-4x+5-3x^{2}=6x-3x^{2}$$

Ikkala tarafdan 6x ni ayirish.

$$-4x+5-3x^{2}-6x=-3x^{2}$$

-10x ni olish uchun -4x va -6x ni birlashtirish.

$$-10x+5-3x^{2}=-3x^{2}$$

3x^{2} ni ikki tarafga qo’shing.

$$-10x+5-3x^{2}+3x^{2}=0$$

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

$$-10x+5=0$$

Ikkala tarafdan 5 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-10x=-5$$

Ikki tarafini -10 ga bo‘ling.

$$x=\frac{-5}{-10}$$

\frac{-5}{-10} ulushini -5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{2}$$