2x+6/3=x^2 eching

$$\frac{ 2x+6 }{ 3 } = { x }^{ 2 }$$

x uchun yechish

$$x = \frac{\sqrt{19} + 1}{3} \approx 1,786299648$$

$$x=\frac{1-\sqrt{19}}{3}\approx -1,119632981$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

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

Ikkala tarafdan 3x^{2} ni ayirish.

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

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.

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

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

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

2 kvadratini chiqarish.

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

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+12\times 6}}{2\left(-3\right)}$$

12 ni 6 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+72}}{2\left(-3\right)}$$

4 ni 72 ga qo'shish.

$$x=\frac{-2±\sqrt{76}}{2\left(-3\right)}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{19}}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{19}}{-6}$$

x=\frac{-2±2\sqrt{19}}{-6} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}-2}{-6}$$

-2+2\sqrt{19} ni -6 ga bo'lish.

$$x=\frac{1-\sqrt{19}}{3}$$

x=\frac{-2±2\sqrt{19}}{-6} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{19} ni ayirish.

$$x=\frac{-2\sqrt{19}-2}{-6}$$

-2-2\sqrt{19} ni -6 ga bo'lish.

$$x=\frac{\sqrt{19}+1}{3}$$

Tenglama yechildi.

$$x=\frac{1-\sqrt{19}}{3} x=\frac{\sqrt{19}+1}{3}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 3 ga ko'paytirish.

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

Ikkala tarafdan 3x^{2} ni ayirish.

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

Ikkala tarafdan 6 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

Ikki tarafini -3 ga bo‘ling.

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

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

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

2 ni -3 ga bo'lish.

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

-6 ni -3 ga bo'lish.

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

-\frac{2}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{3} olish uchun. Keyin, -\frac{1}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{2}{3}x+\left(-\frac{1}{3}\right)^{2}=2+\left(-\frac{1}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{3} kvadratini chiqarish.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=2+\frac{1}{9}$$

2 ni \frac{1}{9} ga qo'shish.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=\frac{19}{9}$$

x^{2}-\frac{2}{3}x+\frac{1}{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.

$$\left(x-\frac{1}{3}\right)^{2}=\frac{19}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{3}\right)^{2}}=\sqrt{\frac{19}{9}}$$

Qisqartirish.

$$x-\frac{1}{3}=\frac{\sqrt{19}}{3} x-\frac{1}{3}=-\frac{\sqrt{19}}{3}$$

\frac{1}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{19}+1}{3} x=\frac{1-\sqrt{19}}{3}$$