x(x-5)+2(x-1)=(x+1)^2 eching

$$x ( x - 5 ) + 2 ( x - 1 ) = ( x + 1 ) ^ { 2 }$$

x uchun yechish

$$x=-\frac{3}{5}=-0,6$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}-5x+2\left(x-1\right)=\left(x+1\right)^{2}$$

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

$$x^{2}-5x+2x-2=\left(x+1\right)^{2}$$

-3x ni olish uchun -5x va 2x ni birlashtirish.

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

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

$$x^{2}-3x-2=x^{2}+2x+1$$

Ikkala tarafdan x^{2} ni ayirish.

$$x^{2}-3x-2-x^{2}=2x+1$$

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

$$-3x-2=2x+1$$

Ikkala tarafdan 2x ni ayirish.

$$-3x-2-2x=1$$

-5x ni olish uchun -3x va -2x ni birlashtirish.

$$-5x-2=1$$

2 ni ikki tarafga qo’shing.

$$-5x=1+2$$

3 olish uchun 1 va 2'ni qo'shing.

$$-5x=3$$

Ikki tarafini -5 ga bo‘ling.

$$x=\frac{3}{-5}$$

\frac{3}{-5} kasri manfiy belgini olib tashlash bilan -\frac{3}{5} sifatida qayta yozilishi mumkin.

$$x=-\frac{3}{5}$$