x^2+6x+13=0 eching

$$x ^ { 2 } + 6 x + 13 = 0$$

x uchun yechish (complex solution)

$$x=-3+2i$$

$$x=-3-2i$$

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.

$$x^{2}+6x+13=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 6 ni b va 13 ni c bilan almashtiring.

$$x=\frac{-6±\sqrt{6^{2}-4\times 13}}{2}$$

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\times 13}}{2}$$

-4 ni 13 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-52}}{2}$$

36 ni -52 ga qo'shish.

$$x=\frac{-6±\sqrt{-16}}{2}$$

-16 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±4i}{2}$$

x=\frac{-6±4i}{2} tenglamasini yeching, bunda ± musbat. -6 ni 4i ga qo'shish.

$$x=\frac{-6+4i}{2}$$

-6+4i ni 2 ga bo'lish.

$$x=-3+2i$$

x=\frac{-6±4i}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 4i ni ayirish.

$$x=\frac{-6-4i}{2}$$

-6-4i ni 2 ga bo'lish.

$$x=-3-2i$$

Tenglama yechildi.

$$x=-3+2i x=-3-2i$$

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.

$$x^{2}+6x+13=0$$

Tenglamaning ikkala tarafidan 13 ni ayirish.

$$x^{2}+6x+13-13=-13$$

O‘zidan 13 ayirilsa 0 qoladi.

$$x^{2}+6x=-13$$

6 ni bo‘lish, x shartining koeffitsienti, 2 ga 3 olish uchun. Keyin, 3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+6x+3^{2}=-13+3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=-13+9$$

-13 ni 9 ga qo'shish.

$$x^{2}+6x+9=-4$$

x^{2}+6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+3\right)^{2}=-4$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{-4}$$

Qisqartirish.

$$x+3=2i x+3=-2i$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=-3+2i x=-3-2i$$