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

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

x uchun yechish

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3,5$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

3x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+6x-\left(x+1\right)\left(x-2\right)=2$$

x+1 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x^{2}-x-2 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}+6x-x^{2}+x+2=2$$

2x^{2} ni olish uchun 3x^{2} va -x^{2} ni birlashtirish.

$$2x^{2}+6x+x+2=2$$

7x ni olish uchun 6x va x ni birlashtirish.

$$2x^{2}+7x+2=2$$

Ikkala tarafdan 2 ni ayirish.

$$2x^{2}+7x+2-2=0$$

0 olish uchun 2 dan 2 ni ayirish.

$$2x^{2}+7x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 7 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-7±\sqrt{7^{2}}}{2\times 2}$$

7^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-7±7}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-7±7}{4}$$

x=\frac{-7±7}{4} tenglamasini yeching, bunda ± musbat. -7 ni 7 ga qo'shish.

$$x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x=0$$

x=\frac{-7±7}{4} tenglamasini yeching, bunda ± manfiy. -7 dan 7 ni ayirish.

$$x=-\frac{14}{4}$$

\frac{-14}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{7}{2}$$

Tenglama yechildi.

$$x=0 x=-\frac{7}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

3x ga x+2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$3x^{2}+6x-\left(x+1\right)\left(x-2\right)=2$$

x+1 ga x-2 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

x^{2}-x-2 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}+6x-x^{2}+x+2=2$$

2x^{2} ni olish uchun 3x^{2} va -x^{2} ni birlashtirish.

$$2x^{2}+6x+x+2=2$$

7x ni olish uchun 6x va x ni birlashtirish.

$$2x^{2}+7x+2=2$$

Ikkala tarafdan 2 ni ayirish.

$$2x^{2}+7x=2-2$$

0 olish uchun 2 dan 2 ni ayirish.

$$2x^{2}+7x=0$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2x^{2}+7x}{2}=\frac{0}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$x^{2}+\frac{7}{2}x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x^{2}+\frac{7}{2}x=0$$

\frac{7}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{4} olish uchun. Keyin, \frac{7}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{7}{2}x+\left(\frac{7}{4}\right)^{2}=\left(\frac{7}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{4} kvadratini chiqarish.

$$x^{2}+\frac{7}{2}x+\frac{49}{16}=\frac{49}{16}$$

x^{2}+\frac{7}{2}x+\frac{49}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{7}{4}\right)^{2}=\frac{49}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{4}\right)^{2}}=\sqrt{\frac{49}{16}}$$

Qisqartirish.

$$x+\frac{7}{4}=\frac{7}{4} x+\frac{7}{4}=-\frac{7}{4}$$

Tenglamaning ikkala tarafidan \frac{7}{4} ni ayirish.

$$x=0 x=-\frac{7}{2}$$