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

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

x uchun yechish

$$x=-4$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

Ikkala tarafdan 2 ni ayirish.

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

0 olish uchun 2 dan 2 ni ayirish.

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

x ni ikki tarafga qo’shing.

$$x^{2}+3x+x=0$$

4x ni olish uchun 3x va x ni birlashtirish.

$$x^{2}+4x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 4 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}}}{2}$$

4^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4}{2}$$

x=\frac{-4±4}{2} tenglamasini yeching, bunda ± musbat. -4 ni 4 ga qo'shish.

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

0 ni 2 ga bo'lish.

$$x=0$$

x=\frac{-4±4}{2} tenglamasini yeching, bunda ± manfiy. -4 dan 4 ni ayirish.

$$x=-\frac{8}{2}$$

-8 ni 2 ga bo'lish.

$$x=-4$$

Tenglama yechildi.

$$x=0 x=-4$$

Kvadratni yakunlash bo'yicha qadamlar

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

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

x ni ikki tarafga qo’shing.

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

4x ni olish uchun 3x va x ni birlashtirish.

$$x^{2}+4x+2=2$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}+4x=2-2$$

0 olish uchun 2 dan 2 ni ayirish.

$$x^{2}+4x=0$$

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

$$x^{2}+4x+2^{2}=2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=4$$

x^{2}+4x+4 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x+2=2 x+2=-2$$

Tenglamaning ikkala tarafidan 2 ni ayirish.

$$x=0 x=-4$$