15*10^-5=x^2/1-x eching

$$15 \times 10 ^ { - 5 } = \frac { x ^ { 2 } } { 1 - x }$$

x uchun yechish

$$x=\frac{\sqrt{240009}-3}{40000}\approx 0,012172678$$

$$x=\frac{-\sqrt{240009}-3}{40000}\approx -0,012322678$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+1 ga ko'paytirish.

$$15\times 10^{-5}\left(-x+1\right)=x^{2}$$

-5 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{100000} ni qiymatni oling.

$$15\times \frac{1}{100000}\left(-x+1\right)=x^{2}$$

\frac{3}{20000} hosil qilish uchun 15 va \frac{1}{100000} ni ko'paytirish.

$$\frac{3}{20000}\left(-x+1\right)=x^{2}$$

\frac{3}{20000} ga -x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{3}{20000}x+\frac{3}{20000}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-\frac{3}{20000}x+\frac{3}{20000}-x^{2}=0$$

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.

$$-x^{2}-\frac{3}{20000}x+\frac{3}{20000}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -\frac{3}{20000} ni b va \frac{3}{20000} ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\left(-\frac{3}{20000}\right)^{2}-4\left(-1\right)\times \frac{3}{20000}}}{2\left(-1\right)}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{20000} kvadratini chiqarish.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{9}{400000000}-4\left(-1\right)\times \frac{3}{20000}}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{9}{400000000}+4\times \frac{3}{20000}}}{2\left(-1\right)}$$

4 ni \frac{3}{20000} marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{9}{400000000}+\frac{3}{5000}}}{2\left(-1\right)}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{9}{400000000} ni \frac{3}{5000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{240009}{400000000}}}{2\left(-1\right)}$$

\frac{240009}{400000000} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\frac{\sqrt{240009}}{20000}}{2\left(-1\right)}$$

-\frac{3}{20000} ning teskarisi \frac{3}{20000} ga teng.

$$x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{-2}$$

x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{-2} tenglamasini yeching, bunda ± musbat. \frac{3}{20000} ni \frac{\sqrt{240009}}{20000} ga qo'shish.

$$x=\frac{\sqrt{240009}+3}{-2\times 20000}$$

\frac{3+\sqrt{240009}}{20000} ni -2 ga bo'lish.

$$x=\frac{-\sqrt{240009}-3}{40000}$$

x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{-2} tenglamasini yeching, bunda ± manfiy. \frac{3}{20000} dan \frac{\sqrt{240009}}{20000} ni ayirish.

$$x=\frac{3-\sqrt{240009}}{-2\times 20000}$$

\frac{3-\sqrt{240009}}{20000} ni -2 ga bo'lish.

$$x=\frac{\sqrt{240009}-3}{40000}$$

Tenglama yechildi.

$$x=\frac{-\sqrt{240009}-3}{40000} x=\frac{\sqrt{240009}-3}{40000}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 1 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+1 ga ko'paytirish.

$$15\times 10^{-5}\left(-x+1\right)=x^{2}$$

-5 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{100000} ni qiymatni oling.

$$15\times \frac{1}{100000}\left(-x+1\right)=x^{2}$$

\frac{3}{20000} hosil qilish uchun 15 va \frac{1}{100000} ni ko'paytirish.

$$\frac{3}{20000}\left(-x+1\right)=x^{2}$$

\frac{3}{20000} ga -x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-\frac{3}{20000}x+\frac{3}{20000}=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-\frac{3}{20000}x+\frac{3}{20000}-x^{2}=0$$

Ikkala tarafdan \frac{3}{20000} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-\frac{3}{20000}x-x^{2}=-\frac{3}{20000}$$

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

$$-x^{2}-\frac{3}{20000}x=-\frac{3}{20000}$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-\frac{3}{20000}x}{-1}=-\frac{\frac{3}{20000}}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{\frac{3}{20000}}{-1}\right)x=-\frac{\frac{3}{20000}}{-1}$$

-\frac{3}{20000} ni -1 ga bo'lish.

$$x^{2}+\frac{3}{20000}x=-\frac{\frac{3}{20000}}{-1}$$

-\frac{3}{20000} ni -1 ga bo'lish.

$$x^{2}+\frac{3}{20000}x=\frac{3}{20000}$$

\frac{3}{20000} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{3}{40000} olish uchun. Keyin, \frac{3}{40000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{3}{20000}x+\left(\frac{3}{40000}\right)^{2}=\frac{3}{20000}+\left(\frac{3}{40000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{3}{40000} kvadratini chiqarish.

$$x^{2}+\frac{3}{20000}x+\frac{9}{1600000000}=\frac{3}{20000}+\frac{9}{1600000000}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{20000} ni \frac{9}{1600000000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{3}{20000}x+\frac{9}{1600000000}=\frac{240009}{1600000000}$$

x^{2}+\frac{3}{20000}x+\frac{9}{1600000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{3}{40000}\right)^{2}=\frac{240009}{1600000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{3}{40000}\right)^{2}}=\sqrt{\frac{240009}{1600000000}}$$

Qisqartirish.

$$x+\frac{3}{40000}=\frac{\sqrt{240009}}{40000} x+\frac{3}{40000}=-\frac{\sqrt{240009}}{40000}$$

Tenglamaning ikkala tarafidan \frac{3}{40000} ni ayirish.

$$x=\frac{\sqrt{240009}-3}{40000} x=\frac{-\sqrt{240009}-3}{40000}$$