x/2=2/3+7/6x eching

$$\frac { x } { 2 } = \frac { 2 } { 3 } + \frac { 7 } { 6 x }$$

x uchun yechish

$$x=-1$$

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2,333333333$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6x ga, 2,3,6x ning eng kichik karralisiga ko‘paytiring.

$$3xx=6x\times \frac{2}{3}+7$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$3x^{2}=6x\times \frac{2}{3}+7$$

4 hosil qilish uchun 6 va \frac{2}{3} ni ko'paytirish.

$$3x^{2}=4x+7$$

Ikkala tarafdan 4x ni ayirish.

$$3x^{2}-4x=7$$

Ikkala tarafdan 7 ni ayirish.

$$3x^{2}-4x-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -4 ni b va -7 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 3\left(-7\right)}}{2\times 3}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 3\left(-7\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-12\left(-7\right)}}{2\times 3}$$

-12 ni -7 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+84}}{2\times 3}$$

16 ni 84 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{100}}{2\times 3}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±10}{2\times 3}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±10}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{4±10}{6}$$

x=\frac{4±10}{6} tenglamasini yeching, bunda ± musbat. 4 ni 10 ga qo'shish.

$$x=\frac{14}{6}$$

\frac{14}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{7}{3}$$

x=\frac{4±10}{6} tenglamasini yeching, bunda ± manfiy. 4 dan 10 ni ayirish.

$$x=-\frac{6}{6}$$

-6 ni 6 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=\frac{7}{3} x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 6x ga, 2,3,6x ning eng kichik karralisiga ko‘paytiring.

$$3xx=6x\times \frac{2}{3}+7$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$3x^{2}=6x\times \frac{2}{3}+7$$

4 hosil qilish uchun 6 va \frac{2}{3} ni ko'paytirish.

$$3x^{2}=4x+7$$

Ikkala tarafdan 4x ni ayirish.

$$3x^{2}-4x=7$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-4x}{3}=\frac{7}{3}$$

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

$$x^{2}-\frac{4}{3}x=\frac{7}{3}$$

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

$$x^{2}-\frac{4}{3}x+\left(-\frac{2}{3}\right)^{2}=\frac{7}{3}+\left(-\frac{2}{3}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{2}{3} kvadratini chiqarish.

$$x^{2}-\frac{4}{3}x+\frac{4}{9}=\frac{7}{3}+\frac{4}{9}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{7}{3} ni \frac{4}{9} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{4}{3}x+\frac{4}{9}=\frac{25}{9}$$

x^{2}-\frac{4}{3}x+\frac{4}{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.

$$\left(x-\frac{2}{3}\right)^{2}=\frac{25}{9}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{2}{3}\right)^{2}}=\sqrt{\frac{25}{9}}$$

Qisqartirish.

$$x-\frac{2}{3}=\frac{5}{3} x-\frac{2}{3}=-\frac{5}{3}$$

\frac{2}{3} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{7}{3} x=-1$$