x^2+4x+6=2x eching

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

x uchun yechish (complex solution)

$$x=-1+\sqrt{5}i\approx -1+2,236067977i$$

$$x=-\sqrt{5}i-1\approx -1-2,236067977i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

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

2x ni olish uchun 4x va -2x ni birlashtirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 2 ni b va 6 ni c bilan almashtiring.

$$x=\frac{-2±\sqrt{2^{2}-4\times 6}}{2}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-24}}{2}$$

4 ni -24 ga qo'shish.

$$x=\frac{-2±\sqrt{-20}}{2}$$

-20 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{5}i}{2}$$

x=\frac{-2±2\sqrt{5}i}{2} tenglamasini yeching, bunda ± musbat. -2 ni 2i\sqrt{5} ga qo'shish.

$$x=\frac{-2+2\sqrt{5}i}{2}$$

-2+2i\sqrt{5} ni 2 ga bo'lish.

$$x=-1+\sqrt{5}i$$

x=\frac{-2±2\sqrt{5}i}{2} tenglamasini yeching, bunda ± manfiy. -2 dan 2i\sqrt{5} ni ayirish.

$$x=\frac{-2\sqrt{5}i-2}{2}$$

-2-2i\sqrt{5} ni 2 ga bo'lish.

$$x=-\sqrt{5}i-1$$

Tenglama yechildi.

$$x=-1+\sqrt{5}i x=-\sqrt{5}i-1$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

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

2x ni olish uchun 4x va -2x ni birlashtirish.

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

Ikkala tarafdan 6 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

2 ni bo‘lish, x shartining koeffitsienti, 2 ga 1 olish uchun. Keyin, 1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+2x+1^{2}=-6+1^{2}$$

1 kvadratini chiqarish.

$$x^{2}+2x+1=-6+1$$

-6 ni 1 ga qo'shish.

$$x^{2}+2x+1=-5$$

x^{2}+2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+1\right)^{2}=-5$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{-5}$$

Qisqartirish.

$$x+1=\sqrt{5}i x+1=-\sqrt{5}i$$

Tenglamaning ikkala tarafidan 1 ni ayirish.

$$x=-1+\sqrt{5}i x=-\sqrt{5}i-1$$