left(3x-7right)^2-5(2x+1)(x-2)=-x^2-(-(3x+1)) eching

$${ \left(3x-7 \right) }^{ 2 } -5(2x+1)(x-2)=- { x }^{ 2 } -(-(3x+1))$$

x uchun yechish

$$x = \frac{29}{15} = 1\frac{14}{15} \approx 1,933333333$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-7\right)^{2} kengaytirilishi uchun ishlating.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)=-x^{2}-\left(-\left(3x+1\right)\right)$$

3x+1 teskarisini topish uchun har birining teskarisini toping.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)=-x^{2}-\left(-3x-1\right)$$

-3x-1 teskarisini topish uchun har birining teskarisini toping.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)=-x^{2}+3x+1$$

x^{2} ni ikki tarafga qo’shing.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)+x^{2}=3x+1$$

Ikkala tarafdan 3x ni ayirish.

$$9x^{2}-42x+49-5\left(2x+1\right)\left(x-2\right)+x^{2}-3x=1$$

-5 ga 2x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x^{2}-42x+49+\left(-10x-5\right)\left(x-2\right)+x^{2}-3x=1$$

-10x-5 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$9x^{2}-42x+49-10x^{2}+15x+10+x^{2}-3x=1$$

-x^{2} ni olish uchun 9x^{2} va -10x^{2} ni birlashtirish.

$$-x^{2}-42x+49+15x+10+x^{2}-3x=1$$

-27x ni olish uchun -42x va 15x ni birlashtirish.

$$-x^{2}-27x+49+10+x^{2}-3x=1$$

59 olish uchun 49 va 10'ni qo'shing.

$$-x^{2}-27x+59+x^{2}-3x=1$$

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

$$-27x+59-3x=1$$

-30x ni olish uchun -27x va -3x ni birlashtirish.

$$-30x+59=1$$

Ikkala tarafdan 59 ni ayirish.

$$-30x=1-59$$

-58 olish uchun 1 dan 59 ni ayirish.

$$-30x=-58$$

Ikki tarafini -30 ga bo‘ling.

$$x=\frac{-58}{-30}$$

\frac{-58}{-30} ulushini -2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{29}{15}$$