x=7/5x-3 eching

$$x = \frac { 7 } { 5 x - 3 }$$

x uchun yechish

$$x = \frac{\sqrt{149} + 3}{10} \approx 1,520655562$$

$$x=\frac{3-\sqrt{149}}{10}\approx -0,920655562$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan \frac{7}{5x-3} ni ayirish.

$$x-\frac{7}{5x-3}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{5x-3}{5x-3} marotabaga ko'paytirish.

$$\frac{x\left(5x-3\right)}{5x-3}-\frac{7}{5x-3}=0$$

\frac{x\left(5x-3\right)}{5x-3} va \frac{7}{5x-3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\left(5x-3\right)-7}{5x-3}=0$$

x\left(5x-3\right)-7 ichidagi ko‘paytirishlarni bajaring.

$$\frac{5x^{2}-3x-7}{5x-3}=0$$

x qiymati \frac{3}{5} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x-3 ga ko'paytirish.

$$5x^{2}-3x-7=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -3 ni b va -7 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 5\left(-7\right)}}{2\times 5}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 5\left(-7\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9-20\left(-7\right)}}{2\times 5}$$

-20 ni -7 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+140}}{2\times 5}$$

9 ni 140 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{149}}{2\times 5}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{149}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{3±\sqrt{149}}{10}$$

x=\frac{3±\sqrt{149}}{10} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{149} ga qo'shish.

$$x=\frac{\sqrt{149}+3}{10}$$

x=\frac{3±\sqrt{149}}{10} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{149} ni ayirish.

$$x=\frac{3-\sqrt{149}}{10}$$

Tenglama yechildi.

$$x=\frac{\sqrt{149}+3}{10} x=\frac{3-\sqrt{149}}{10}$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan \frac{7}{5x-3} ni ayirish.

$$x-\frac{7}{5x-3}=0$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{5x-3}{5x-3} marotabaga ko'paytirish.

$$\frac{x\left(5x-3\right)}{5x-3}-\frac{7}{5x-3}=0$$

\frac{x\left(5x-3\right)}{5x-3} va \frac{7}{5x-3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\left(5x-3\right)-7}{5x-3}=0$$

x\left(5x-3\right)-7 ichidagi ko‘paytirishlarni bajaring.

$$\frac{5x^{2}-3x-7}{5x-3}=0$$

x qiymati \frac{3}{5} teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini 5x-3 ga ko'paytirish.

$$5x^{2}-3x-7=0$$

7 ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$5x^{2}-3x=7$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-3x}{5}=\frac{7}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{3}{5}x=\frac{7}{5}$$

-\frac{3}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{10} olish uchun. Keyin, -\frac{3}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{3}{5}x+\left(-\frac{3}{10}\right)^{2}=\frac{7}{5}+\left(-\frac{3}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{10} kvadratini chiqarish.

$$x^{2}-\frac{3}{5}x+\frac{9}{100}=\frac{7}{5}+\frac{9}{100}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{7}{5} ni \frac{9}{100} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{3}{5}x+\frac{9}{100}=\frac{149}{100}$$

x^{2}-\frac{3}{5}x+\frac{9}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{10}\right)^{2}=\frac{149}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{10}\right)^{2}}=\sqrt{\frac{149}{100}}$$

Qisqartirish.

$$x-\frac{3}{10}=\frac{\sqrt{149}}{10} x-\frac{3}{10}=-\frac{\sqrt{149}}{10}$$

\frac{3}{10} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{149}+3}{10} x=\frac{3-\sqrt{149}}{10}$$