x^2+6x+36=0 eching

$${ x }^{ 2 } +6x+36=0$$

x uchun yechish (complex solution)

$$x=-3+3\sqrt{3}i\approx -3+5,196152423i$$

$$x=-3\sqrt{3}i-3\approx -3-5,196152423i$$

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.

$$x^{2}+6x+36=0$$

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 36 ni c bilan almashtiring.

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

6 kvadratini chiqarish.

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

-4 ni 36 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-144}}{2}$$

36 ni -144 ga qo'shish.

$$x=\frac{-6±\sqrt{-108}}{2}$$

-108 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±6\sqrt{3}i}{2}$$

x=\frac{-6±6\sqrt{3}i}{2} tenglamasini yeching, bunda ± musbat. -6 ni 6i\sqrt{3} ga qo'shish.

$$x=\frac{-6+6\sqrt{3}i}{2}$$

-6+6i\sqrt{3} ni 2 ga bo'lish.

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

x=\frac{-6±6\sqrt{3}i}{2} tenglamasini yeching, bunda ± manfiy. -6 dan 6i\sqrt{3} ni ayirish.

$$x=\frac{-6\sqrt{3}i-6}{2}$$

-6-6i\sqrt{3} ni 2 ga bo'lish.

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

Tenglama yechildi.

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

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.

$$x^{2}+6x+36=0$$

Tenglamaning ikkala tarafidan 36 ni ayirish.

$$x^{2}+6x+36-36=-36$$

O‘zidan 36 ayirilsa 0 qoladi.

$$x^{2}+6x=-36$$

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.

$$x^{2}+6x+3^{2}=-36+3^{2}$$

3 kvadratini chiqarish.

$$x^{2}+6x+9=-36+9$$

-36 ni 9 ga qo'shish.

$$x^{2}+6x+9=-27$$

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.

$$\left(x+3\right)^{2}=-27$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{-27}$$

Qisqartirish.

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

Tenglamaning ikkala tarafidan 3 ni ayirish.

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