x^2+12x+37=0 eching

$$x ^ { 2 } + 12 x + 37 = 0$$

x uchun yechish (complex solution)

$$x=-6+i$$

$$x=-6-i$$

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.

$$x^{2}+12x+37=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 12 ni b va 37 ni c bilan almashtiring.

$$x=\frac{-12±\sqrt{12^{2}-4\times 37}}{2}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 37}}{2}$$

-4 ni 37 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-148}}{2}$$

144 ni -148 ga qo'shish.

$$x=\frac{-12±\sqrt{-4}}{2}$$

-4 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±2i}{2}$$

x=\frac{-12±2i}{2} tenglamasini yeching, bunda ± musbat. -12 ni 2i ga qo'shish.

$$x=\frac{-12+2i}{2}$$

-12+2i ni 2 ga bo'lish.

$$x=-6+i$$

x=\frac{-12±2i}{2} tenglamasini yeching, bunda ± manfiy. -12 dan 2i ni ayirish.

$$x=\frac{-12-2i}{2}$$

-12-2i ni 2 ga bo'lish.

$$x=-6-i$$

Tenglama yechildi.

$$x=-6+i x=-6-i$$

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.

$$x^{2}+12x+37=0$$

Tenglamaning ikkala tarafidan 37 ni ayirish.

$$x^{2}+12x+37-37=-37$$

O‘zidan 37 ayirilsa 0 qoladi.

$$x^{2}+12x=-37$$

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

$$x^{2}+12x+6^{2}=-37+6^{2}$$

6 kvadratini chiqarish.

$$x^{2}+12x+36=-37+36$$

-37 ni 36 ga qo'shish.

$$x^{2}+12x+36=-1$$

x^{2}+12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+6\right)^{2}=-1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{-1}$$

Qisqartirish.

$$x+6=i x+6=-i$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$x=-6+i x=-6-i$$