(x+3)^2+(x+5)(x-2)+4=2(x+7)(x-3) eching

$$( x + 3 ) ^ { 2 } + ( x + 5 ) ( x - 2 ) + 4 = 2 ( x + 7 ) ( x - 3 )$$

x uchun yechish

$$x=-45$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}+6x+9+\left(x+5\right)\left(x-2\right)+4=2\left(x+7\right)\left(x-3\right)$$

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

$$x^{2}+6x+9+x^{2}+3x-10+4=2\left(x+7\right)\left(x-3\right)$$

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

$$2x^{2}+6x+9+3x-10+4=2\left(x+7\right)\left(x-3\right)$$

9x ni olish uchun 6x va 3x ni birlashtirish.

$$2x^{2}+9x+9-10+4=2\left(x+7\right)\left(x-3\right)$$

-1 olish uchun 9 dan 10 ni ayirish.

$$2x^{2}+9x-1+4=2\left(x+7\right)\left(x-3\right)$$

3 olish uchun -1 va 4'ni qo'shing.

$$2x^{2}+9x+3=2\left(x+7\right)\left(x-3\right)$$

2 ga x+7 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+9x+3=\left(2x+14\right)\left(x-3\right)$$

2x+14 ga x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+9x+3=2x^{2}+8x-42$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2x^{2}+9x+3-2x^{2}=8x-42$$

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

$$9x+3=8x-42$$

Ikkala tarafdan 8x ni ayirish.

$$9x+3-8x=-42$$

x ni olish uchun 9x va -8x ni birlashtirish.

$$x+3=-42$$

Ikkala tarafdan 3 ni ayirish.

$$x=-42-3$$

-45 olish uchun -42 dan 3 ni ayirish.

$$x=-45$$