3x+2/6*x+2/3=0 eching

$$\frac { 3 x + 2 } { 6 } \times \frac { x + 2 } { 3 } = 0$$

x uchun yechish

$$x=-2$$

$$x=-\frac{2}{3}\approx -0,666666667$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 6 ga, 6,3 ning eng kichik karralisiga ko‘paytiring.

$$\left(3x+2\right)\times \frac{x+2}{3}=0$$

\left(3x+2\right)\times \frac{x+2}{3} ni yagona kasrga aylantiring.

$$\frac{\left(3x+2\right)\left(x+2\right)}{3}=0$$

3x+2 ifodaning har bir elementini x+2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{3x^{2}+6x+2x+4}{3}=0$$

8x ni olish uchun 6x va 2x ni birlashtirish.

$$\frac{3x^{2}+8x+4}{3}=0$$

x^{2}+\frac{8}{3}x+\frac{4}{3} natijani olish uchun 3x^{2}+8x+4 ning har bir ifodasini 3 ga bo‘ling.

$$x^{2}+\frac{8}{3}x+\frac{4}{3}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, \frac{8}{3} ni b va \frac{4}{3} ni c bilan almashtiring.

$$x=\frac{-\frac{8}{3}±\sqrt{\left(\frac{8}{3}\right)^{2}-4\times \frac{4}{3}}}{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{8}{3} kvadratini chiqarish.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{64}{9}-4\times \frac{4}{3}}}{2}$$

-4 ni \frac{4}{3} marotabaga ko'paytirish.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{64}{9}-\frac{16}{3}}}{2}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{64}{9} ni -\frac{16}{3} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{-\frac{8}{3}±\sqrt{\frac{16}{9}}}{2}$$

\frac{16}{9} ning kvadrat ildizini chiqarish.

$$x=\frac{-\frac{8}{3}±\frac{4}{3}}{2}$$

x=\frac{-\frac{8}{3}±\frac{4}{3}}{2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{8}{3} ni \frac{4}{3} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=-\frac{\frac{4}{3}}{2}$$

-\frac{4}{3} ni 2 ga bo'lish.

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

x=\frac{-\frac{8}{3}±\frac{4}{3}}{2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{4}{3} ni -\frac{8}{3} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=-\frac{4}{2}$$

-4 ni 2 ga bo'lish.

$$x=-2$$

Tenglama yechildi.

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

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 6 ga, 6,3 ning eng kichik karralisiga ko‘paytiring.

$$\left(3x+2\right)\times \frac{x+2}{3}=0$$

\left(3x+2\right)\times \frac{x+2}{3} ni yagona kasrga aylantiring.

$$\frac{\left(3x+2\right)\left(x+2\right)}{3}=0$$

3x+2 ifodaning har bir elementini x+2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{3x^{2}+6x+2x+4}{3}=0$$

8x ni olish uchun 6x va 2x ni birlashtirish.

$$\frac{3x^{2}+8x+4}{3}=0$$

x^{2}+\frac{8}{3}x+\frac{4}{3} natijani olish uchun 3x^{2}+8x+4 ning har bir ifodasini 3 ga bo‘ling.

$$x^{2}+\frac{8}{3}x+\frac{4}{3}=0$$

Ikkala tarafdan \frac{4}{3} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}+\frac{8}{3}x=-\frac{4}{3}$$

\frac{8}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{4}{3} olish uchun. Keyin, \frac{4}{3} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{8}{3}x+\left(\frac{4}{3}\right)^{2}=-\frac{4}{3}+\left(\frac{4}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{4}{3} kvadratini chiqarish.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=-\frac{4}{3}+\frac{16}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{4}{3} ni \frac{16}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=\frac{4}{9}$$

x^{2}+\frac{8}{3}x+\frac{16}{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.

$$\left(x+\frac{4}{3}\right)^{2}=\frac{4}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{4}{3}\right)^{2}}=\sqrt{\frac{4}{9}}$$

Qisqartirish.

$$x+\frac{4}{3}=\frac{2}{3} x+\frac{4}{3}=-\frac{2}{3}$$

Tenglamaning ikkala tarafidan \frac{4}{3} ni ayirish.

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