5left(2x+6right)left(2x-6right)+4left(3x-1right)^2=left(7x-10right)left(8x+3right)-6 eching

$$5 \left( 2x+6 \right) \left( 2x-6 \right) +4 { \left(3x-1 \right) }^{ 2 } = \left( 7x-10 \right) \left( 8x+3 \right) -6$$

x uchun yechish

$$x=4$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

5 ga 2x+6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(10x+30\right)\left(2x-6\right)+4\left(3x-1\right)^{2}=\left(7x-10\right)\left(8x+3\right)-6$$

10x+30 ga 2x-6 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$20x^{2}-180+4\left(3x-1\right)^{2}=\left(7x-10\right)\left(8x+3\right)-6$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-1\right)^{2} kengaytirilishi uchun ishlating.

$$20x^{2}-180+4\left(9x^{2}-6x+1\right)=\left(7x-10\right)\left(8x+3\right)-6$$

4 ga 9x^{2}-6x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$20x^{2}-180+36x^{2}-24x+4=\left(7x-10\right)\left(8x+3\right)-6$$

56x^{2} ni olish uchun 20x^{2} va 36x^{2} ni birlashtirish.

$$56x^{2}-180-24x+4=\left(7x-10\right)\left(8x+3\right)-6$$

-176 olish uchun -180 va 4'ni qo'shing.

$$56x^{2}-176-24x=\left(7x-10\right)\left(8x+3\right)-6$$

7x-10 ga 8x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$56x^{2}-176-24x=56x^{2}-59x-30-6$$

-36 olish uchun -30 dan 6 ni ayirish.

$$56x^{2}-176-24x=56x^{2}-59x-36$$

Ikkala tarafdan 56x^{2} ni ayirish.

$$56x^{2}-176-24x-56x^{2}=-59x-36$$

0 ni olish uchun 56x^{2} va -56x^{2} ni birlashtirish.

$$-176-24x=-59x-36$$

59x ni ikki tarafga qo’shing.

$$-176-24x+59x=-36$$

35x ni olish uchun -24x va 59x ni birlashtirish.

$$-176+35x=-36$$

176 ni ikki tarafga qo’shing.

$$35x=-36+176$$

140 olish uchun -36 va 176'ni qo'shing.

$$35x=140$$

Ikki tarafini 35 ga bo‘ling.

$$x=\frac{140}{35}$$

4 ni olish uchun 140 ni 35 ga bo‘ling.

$$x=4$$