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

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

x uchun yechish (complex solution)

$$x=-2+2i$$

$$x=-2-2i$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$x^{2}+5x+6=x-2$$

Ikkala tarafdan x ni ayirish.

$$x^{2}+5x+6-x=-2$$

4x ni olish uchun 5x va -x ni birlashtirish.

$$x^{2}+4x+6=-2$$

2 ni ikki tarafga qo’shing.

$$x^{2}+4x+6+2=0$$

8 olish uchun 6 va 2'ni qo'shing.

$$x^{2}+4x+8=0$$

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 8 ni c bilan almashtiring.

$$x=\frac{-4±\sqrt{4^{2}-4\times 8}}{2}$$

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\times 8}}{2}$$

-4 ni 8 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-32}}{2}$$

16 ni -32 ga qo'shish.

$$x=\frac{-4±\sqrt{-16}}{2}$$

-16 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±4i}{2}$$

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

$$x=\frac{-4+4i}{2}$$

-4+4i ni 2 ga bo'lish.

$$x=-2+2i$$

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

$$x=\frac{-4-4i}{2}$$

-4-4i ni 2 ga bo'lish.

$$x=-2-2i$$

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

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

$$x^{2}+5x+6=x-2$$

Ikkala tarafdan x ni ayirish.

$$x^{2}+5x+6-x=-2$$

4x ni olish uchun 5x va -x ni birlashtirish.

$$x^{2}+4x+6=-2$$

Ikkala tarafdan 6 ni ayirish.

$$x^{2}+4x=-2-6$$

-8 olish uchun -2 dan 6 ni ayirish.

$$x^{2}+4x=-8$$

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.

$$x^{2}+4x+2^{2}=-8+2^{2}$$

2 kvadratini chiqarish.

$$x^{2}+4x+4=-8+4$$

-8 ni 4 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

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