x^2+6x+2=0 eching

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

x uchun yechish (complex solution)

$$x=\sqrt{7}-3\approx -0,354248689$$

$$x=-\left(\sqrt{7}+3\right)\approx -5,645751311$$

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.

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

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 2 ni c bilan almashtiring.

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

6 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-8}}{2}$$

36 ni -8 ga qo'shish.

$$x=\frac{-6±\sqrt{28}}{2}$$

28 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{7}}{2}$$

x=\frac{-6±2\sqrt{7}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{7} ga qo'shish.

$$x=\frac{2\sqrt{7}-6}{2}$$

-6+2\sqrt{7} ni 2 ga bo'lish.

$$x=\sqrt{7}-3$$

x=\frac{-6±2\sqrt{7}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{7} ni ayirish.

$$x=\frac{-2\sqrt{7}-6}{2}$$

-6-2\sqrt{7} ni 2 ga bo'lish.

$$x=-\sqrt{7}-3$$

Tenglama yechildi.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$

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.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

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

O‘zidan 2 ayirilsa 0 qoladi.

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

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.

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

3 kvadratini chiqarish.

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

-2 ni 9 ga qo'shish.

$$x^{2}+6x+9=7$$

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.

$$\left(x+3\right)^{2}=7$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{7}$$

Qisqartirish.

$$x+3=\sqrt{7} x+3=-\sqrt{7}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$

x uchun yechish

$$x=\sqrt{7}-3\approx -0,354248689$$

$$x=-\sqrt{7}-3\approx -5,645751311$$

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.

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

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 2 ni c bilan almashtiring.

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

6 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-8}}{2}$$

36 ni -8 ga qo'shish.

$$x=\frac{-6±\sqrt{28}}{2}$$

28 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{7}}{2}$$

x=\frac{-6±2\sqrt{7}}{2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{7} ga qo'shish.

$$x=\frac{2\sqrt{7}-6}{2}$$

-6+2\sqrt{7} ni 2 ga bo'lish.

$$x=\sqrt{7}-3$$

x=\frac{-6±2\sqrt{7}}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{7} ni ayirish.

$$x=\frac{-2\sqrt{7}-6}{2}$$

-6-2\sqrt{7} ni 2 ga bo'lish.

$$x=-\sqrt{7}-3$$

Tenglama yechildi.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$

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.

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

Tenglamaning ikkala tarafidan 2 ni ayirish.

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

O‘zidan 2 ayirilsa 0 qoladi.

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

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.

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

3 kvadratini chiqarish.

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

-2 ni 9 ga qo'shish.

$$x^{2}+6x+9=7$$

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.

$$\left(x+3\right)^{2}=7$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{7}$$

Qisqartirish.

$$x+3=\sqrt{7} x+3=-\sqrt{7}$$

Tenglamaning ikkala tarafidan 3 ni ayirish.

$$x=\sqrt{7}-3 x=-\sqrt{7}-3$$