x^2+4x+6=0 eching

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

x uchun yechish (complex solution)

$$x=-2+\sqrt{2}i\approx -2+1,414213562i$$

$$x=-\sqrt{2}i-2\approx -2-1,414213562i$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

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

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 6 ni c bilan almashtiring.

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

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\times 6}}{2}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-24}}{2}$$

16 ni -24 ga qo'shish.

$$x=\frac{-4±\sqrt{-8}}{2}$$

-8 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{2}i}{2}$$

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

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

-4+2i\sqrt{2} ni 2 ga bo'lish.

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

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

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

-4-2i\sqrt{2} ni 2 ga bo'lish.

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

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Tenglamaning ikkala tarafidan 6 ni ayirish.

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

O‘zidan 6 ayirilsa 0 qoladi.

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

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.

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

2 kvadratini chiqarish.

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

-6 ni 4 ga qo'shish.

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

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.

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

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