3x^2-6x+36=0 eching

$$3 { x }^{ 2 } -6x+36=0$$

x uchun yechish (complex solution)

$$x=1+\sqrt{11}i\approx 1+3,31662479i$$

$$x=-\sqrt{11}i+1\approx 1-3,31662479i$$

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.

$$3x^{2}-6x+36=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -6 ni b va 36 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 3\times 36}}{2\times 3}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 3\times 36}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-12\times 36}}{2\times 3}$$

-12 ni 36 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36-432}}{2\times 3}$$

36 ni -432 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{-396}}{2\times 3}$$

-396 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±6\sqrt{11}i}{2\times 3}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±6\sqrt{11}i}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{6±6\sqrt{11}i}{6}$$

x=\frac{6±6\sqrt{11}i}{6} tenglamasini yeching, bunda ± musbat. 6 ni 6i\sqrt{11} ga qo'shish.

$$x=\frac{6+6\sqrt{11}i}{6}$$

6+6i\sqrt{11} ni 6 ga bo'lish.

$$x=1+\sqrt{11}i$$

x=\frac{6±6\sqrt{11}i}{6} tenglamasini yeching, bunda ± manfiy. 6 dan 6i\sqrt{11} ni ayirish.

$$x=\frac{-6\sqrt{11}i+6}{6}$$

6-6i\sqrt{11} ni 6 ga bo'lish.

$$x=-\sqrt{11}i+1$$

Tenglama yechildi.

$$x=1+\sqrt{11}i x=-\sqrt{11}i+1$$

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.

$$3x^{2}-6x+36=0$$

Tenglamaning ikkala tarafidan 36 ni ayirish.

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

O‘zidan 36 ayirilsa 0 qoladi.

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

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-6x}{3}=-\frac{36}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{6}{3}\right)x=-\frac{36}{3}$$

-6 ni 3 ga bo'lish.

$$x^{2}-2x=-\frac{36}{3}$$

-36 ni 3 ga bo'lish.

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

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

-12 ni 1 ga qo'shish.

$$x^{2}-2x+1=-11$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=-11$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{-11}$$

Qisqartirish.

$$x-1=\sqrt{11}i x-1=-\sqrt{11}i$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=1+\sqrt{11}i x=-\sqrt{11}i+1$$