3x(x+1)-x=2(x+54) eching

$$3x(x+1)-x=2(x+54)$$

x uchun yechish

$$x=-6$$

$$x=6$$

Kvadrat ildizini topish bo'yicha qadamlar

3x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+3x-x=2\left(x+54\right)$$

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

$$3x^{2}+2x=2\left(x+54\right)$$

2 ga x+54 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+2x=2x+108$$

Ikkala tarafdan 2x ni ayirish.

$$3x^{2}+2x-2x=108$$

0 ni olish uchun 2x va -2x ni birlashtirish.

$$3x^{2}=108$$

Ikki tarafini 3 ga bo‘ling.

$$x^{2}=\frac{108}{3}$$

36 ni olish uchun 108 ni 3 ga bo‘ling.

$$x^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=6 x=-6$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+3x-x=2\left(x+54\right)$$

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

$$3x^{2}+2x=2\left(x+54\right)$$

2 ga x+54 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+2x=2x+108$$

Ikkala tarafdan 2x ni ayirish.

$$3x^{2}+2x-2x=108$$

0 ni olish uchun 2x va -2x ni birlashtirish.

$$3x^{2}=108$$

Ikkala tarafdan 108 ni ayirish.

$$3x^{2}-108=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, 0 ni b va -108 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-108\right)}}{2\times 3}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 3\left(-108\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-12\left(-108\right)}}{2\times 3}$$

-12 ni -108 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{1296}}{2\times 3}$$

1296 ning kvadrat ildizini chiqarish.

$$x=\frac{0±36}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{0±36}{6}$$

x=\frac{0±36}{6} tenglamasini yeching, bunda ± musbat. 36 ni 6 ga bo'lish.

$$x=6$$

x=\frac{0±36}{6} tenglamasini yeching, bunda ± manfiy. -36 ni 6 ga bo'lish.

$$x=-6$$

Tenglama yechildi.

$$x=6 x=-6$$