5-x/4*10^6=96x-x^2 eching

$$\frac { 5 - x } { 4 \times 10 ^ { 6 } } = 96 x - x ^ { 2 }$$

x uchun yechish

$$x = \frac{\sqrt{147456000688000001} + 384000001}{8000000} \approx 96,000000237$$

$$x=\frac{384000001-\sqrt{147456000688000001}}{8000000}\approx 0,000000013$$

Kvadrat tenglamalaridan foydalanish qoidalari

6 daraja ko‘rsatkichini 10 ga hisoblang va 1000000 ni qiymatni oling.

$$\frac{5-x}{4\times 1000000}=96x-x^{2}$$

4000000 hosil qilish uchun 4 va 1000000 ni ko'paytirish.

$$\frac{5-x}{4000000}=96x-x^{2}$$

\frac{1}{800000}-\frac{1}{4000000}x natijani olish uchun 5-x ning har bir ifodasini 4000000 ga bo‘ling.

$$\frac{1}{800000}-\frac{1}{4000000}x=96x-x^{2}$$

Ikkala tarafdan 96x ni ayirish.

$$\frac{1}{800000}-\frac{1}{4000000}x-96x=-x^{2}$$

-\frac{384000001}{4000000}x ni olish uchun -\frac{1}{4000000}x va -96x ni birlashtirish.

$$\frac{1}{800000}-\frac{384000001}{4000000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{1}{800000}-\frac{384000001}{4000000}x+x^{2}=0$$

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.

$$x^{2}-\frac{384000001}{4000000}x+\frac{1}{800000}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -\frac{384000001}{4000000} ni b va \frac{1}{800000} ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\left(-\frac{384000001}{4000000}\right)^{2}-4\times \frac{1}{800000}}}{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{384000001}{4000000} kvadratini chiqarish.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000768000001}{16000000000000}-4\times \frac{1}{800000}}}{2}$$

-4 ni \frac{1}{800000} marotabaga ko'paytirish.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000768000001}{16000000000000}-\frac{1}{200000}}}{2}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{147456000768000001}{16000000000000} ni -\frac{1}{200000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000688000001}{16000000000000}}}{2}$$

\frac{147456000688000001}{16000000000000} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\frac{\sqrt{147456000688000001}}{4000000}}{2}$$

-\frac{384000001}{4000000} ning teskarisi \frac{384000001}{4000000} ga teng.

$$x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2}$$

x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2} tenglamasini yeching, bunda ± musbat. \frac{384000001}{4000000} ni \frac{\sqrt{147456000688000001}}{4000000} ga qo'shish.

$$x=\frac{\sqrt{147456000688000001}[phone]}{2\times 4000000}$$

\frac{384000001+\sqrt{147456000688000001}}{4000000} ni 2 ga bo'lish.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000}$$

x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2} tenglamasini yeching, bunda ± manfiy. \frac{384000001}{4000000} dan \frac{\sqrt{147456000688000001}}{4000000} ni ayirish.

$$x=\frac{384000001-\sqrt{147456000688000001}}{2\times 4000000}$$

\frac{384000001-\sqrt{147456000688000001}}{4000000} ni 2 ga bo'lish.

$$x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$

Tenglama yechildi.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000} x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$

Kvadratni yakunlash bo'yicha qadamlar

6 daraja ko‘rsatkichini 10 ga hisoblang va 1000000 ni qiymatni oling.

$$\frac{5-x}{4\times 1000000}=96x-x^{2}$$

4000000 hosil qilish uchun 4 va 1000000 ni ko'paytirish.

$$\frac{5-x}{4000000}=96x-x^{2}$$

\frac{1}{800000}-\frac{1}{4000000}x natijani olish uchun 5-x ning har bir ifodasini 4000000 ga bo‘ling.

$$\frac{1}{800000}-\frac{1}{4000000}x=96x-x^{2}$$

Ikkala tarafdan 96x ni ayirish.

$$\frac{1}{800000}-\frac{1}{4000000}x-96x=-x^{2}$$

-\frac{384000001}{4000000}x ni olish uchun -\frac{1}{4000000}x va -96x ni birlashtirish.

$$\frac{1}{800000}-\frac{384000001}{4000000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{1}{800000}-\frac{384000001}{4000000}x+x^{2}=0$$

Ikkala tarafdan \frac{1}{800000} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$-\frac{384000001}{4000000}x+x^{2}=-\frac{1}{800000}$$

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

$$x^{2}-\frac{384000001}{4000000}x=-\frac{1}{800000}$$

-\frac{384000001}{4000000} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{384000001}{8000000} olish uchun. Keyin, -\frac{384000001}{8000000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{384000001}{4000000}x+\left(-\frac{384000001}{8000000}\right)^{2}=-\frac{1}{800000}+\left(-\frac{384000001}{8000000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{384000001}{8000000} kvadratini chiqarish.

$$x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}=-\frac{1}{800000}+\frac{147456000768000001}{64000000000000}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{1}{800000} ni \frac{147456000768000001}{64000000000000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}=\frac{147456000688000001}{64000000000000}$$

x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{384000001}{8000000}\right)^{2}=\frac{147456000688000001}{64000000000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{384000001}{8000000}\right)^{2}}=\sqrt{\frac{147456000688000001}{64000000000000}}$$

Qisqartirish.

$$x-\frac{384000001}{8000000}=\frac{\sqrt{147456000688000001}}{8000000} x-\frac{384000001}{8000000}=-\frac{\sqrt{147456000688000001}}{8000000}$$

\frac{384000001}{8000000} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000} x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$