1044*10^-3p=83145*29815(1-186*10^-6p+106*10^-8p^2) eching

$$1044 \times 10 ^ { - 3 } p = 83145 \times 29815 ( 1 - 186 \times 10 ^ { - 6 } p + 106 \times 10 ^ { - 8 } p ^ { 2 } )$$

p uchun yechish

$$p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177}\approx 87,736047709+967,315156682i$$

$$p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177}\approx 87,736047709-967,315156682i$$

Kvadrat tenglamalaridan foydalanish qoidalari

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$1044\times \frac{1}{1000}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

\frac{261}{250} hosil qilish uchun 1044 va \frac{1}{1000} ni ko'paytirish.

$$\frac{261}{250}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

2478968175 hosil qilish uchun 83145 va 29815 ni ko'paytirish.

$$\frac{261}{250}p=2478968175\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

-6 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000000} ni qiymatni oling.

$$\frac{261}{250}p=2478968175\left(1-186\times \frac{1}{1000000}p+106\times 10^{-8}p^{2}\right)$$

\frac{93}{500000} hosil qilish uchun 186 va \frac{1}{1000000} ni ko'paytirish.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times 10^{-8}p^{2}\right)$$

-8 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{100000000} ni qiymatni oling.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times \frac{1}{100000000}p^{2}\right)$$

\frac{53}{50000000} hosil qilish uchun 106 va \frac{1}{100000000} ni ko'paytirish.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}\right)$$

2478968175 ga 1-\frac{93}{500000}p+\frac{53}{50000000}p^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{261}{250}p=2478968175-\frac{9221761611}{20000}p+\frac{5255412531}{2000000}p^{2}$$

Ikkala tarafdan 2478968175 ni ayirish.

$$\frac{261}{250}p-2478968175=-\frac{9221761611}{20000}p+\frac{5255412531}{2000000}p^{2}$$

\frac{9221761611}{20000}p ni ikki tarafga qo’shing.

$$\frac{261}{250}p-2478968175+\frac{9221761611}{20000}p=\frac{5255412531}{2000000}p^{2}$$

\frac{9221782491}{20000}p ni olish uchun \frac{261}{250}p va \frac{9221761611}{20000}p ni birlashtirish.

$$\frac{9221782491}{20000}p-2478968175=\frac{5255412531}{2000000}p^{2}$$

Ikkala tarafdan \frac{5255412531}{2000000}p^{2} ni ayirish.

$$\frac{9221782491}{20000}p-2478968175-\frac{5255412531}{2000000}p^{2}=0$$

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.

$$-\frac{5255412531}{2000000}p^{2}+\frac{9221782491}{20000}p-2478968175=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -\frac{5255412531}{2000000} ni a, \frac{9221782491}{20000} ni b va -2478968175 ni c bilan almashtiring.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\left(\frac{9221782491}{20000}\right)^{2}-4\left(-\frac{5255412531}{2000000}\right)\left(-2478968175\right)}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9221782491}{20000} kvadratini chiqarish.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\frac{85041272311314165081}{400000000}-4\left(-\frac{5255412531}{2000000}\right)\left(-2478968175\right)}}{2\left(-\frac{5255412531}{2000000}\right)}$$

-4 ni -\frac{5255412531}{2000000} marotabaga ko'paytirish.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\frac{85041272311314165081}{400000000}+\frac{5255412531}{500000}\left(-2478968175\right)}}{2\left(-\frac{5255412531}{2000000}\right)}$$

\frac{5255412531}{500000} ni -2478968175 marotabaga ko'paytirish.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\frac{85041272311314165081}{400000000}-\frac{521120016433808037}{20000}}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{85041272311314165081}{400000000} ni -\frac{521120016433808037}{20000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{-\frac{10337359056364846574919}{400000000}}}{2\left(-\frac{5255412531}{2000000}\right)}$$

-\frac{10337359056364846574919}{400000000} ning kvadrat ildizini chiqarish.

$$p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{2\left(-\frac{5255412531}{2000000}\right)}$$

2 ni -\frac{5255412531}{2000000} marotabaga ko'paytirish.

$$p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}}$$

p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}} tenglamasini yeching, bunda ± musbat. -\frac{9221782491}{20000} ni \frac{3i\sqrt{1148595450707205174991}}{20000} ga qo'shish.

$$p=\frac{-9221782491+3\sqrt{1148595450707205174991}i}{-\frac{5255412531}{1000000}\times 20000}$$

\frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} ni -\frac{5255412531}{1000000} ga bo'lish \frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} ga k'paytirish -\frac{5255412531}{1000000} ga qaytarish.

$$p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177}$$

p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}} tenglamasini yeching, bunda ± manfiy. -\frac{9221782491}{20000} dan \frac{3i\sqrt{1148595450707205174991}}{20000} ni ayirish.

$$p=\frac{-3\sqrt{1148595450707205174991}i-9221782491}{-\frac{5255412531}{1000000}\times 20000}$$

\frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} ni -\frac{5255412531}{1000000} ga bo'lish \frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} ga k'paytirish -\frac{5255412531}{1000000} ga qaytarish.

$$p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177}$$

Tenglama yechildi.

$$p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177} p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177}$$

Kvadratni yakunlash bo'yicha qadamlar

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$1044\times \frac{1}{1000}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

\frac{261}{250} hosil qilish uchun 1044 va \frac{1}{1000} ni ko'paytirish.

$$\frac{261}{250}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

2478968175 hosil qilish uchun 83145 va 29815 ni ko'paytirish.

$$\frac{261}{250}p=2478968175\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

-6 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000000} ni qiymatni oling.

$$\frac{261}{250}p=2478968175\left(1-186\times \frac{1}{1000000}p+106\times 10^{-8}p^{2}\right)$$

\frac{93}{500000} hosil qilish uchun 186 va \frac{1}{1000000} ni ko'paytirish.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times 10^{-8}p^{2}\right)$$

-8 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{100000000} ni qiymatni oling.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times \frac{1}{100000000}p^{2}\right)$$

\frac{53}{50000000} hosil qilish uchun 106 va \frac{1}{100000000} ni ko'paytirish.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}\right)$$

2478968175 ga 1-\frac{93}{500000}p+\frac{53}{50000000}p^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{261}{250}p=2478968175-\frac{9221761611}{20000}p+\frac{5255412531}{2000000}p^{2}$$

\frac{9221761611}{20000}p ni ikki tarafga qo’shing.

$$\frac{261}{250}p+\frac{9221761611}{20000}p=2478968175+\frac{5255412531}{2000000}p^{2}$$

\frac{9221782491}{20000}p ni olish uchun \frac{261}{250}p va \frac{9221761611}{20000}p ni birlashtirish.

$$\frac{9221782491}{20000}p=2478968175+\frac{5255412531}{2000000}p^{2}$$

Ikkala tarafdan \frac{5255412531}{2000000}p^{2} ni ayirish.

$$\frac{9221782491}{20000}p-\frac{5255412531}{2000000}p^{2}=2478968175$$

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

$$-\frac{5255412531}{2000000}p^{2}+\frac{9221782491}{20000}p=2478968175$$

Tenglamaning ikki tarafini -\frac{5255412531}{2000000} ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{-\frac{5255412531}{2000000}p^{2}+\frac{9221782491}{20000}p}{-\frac{5255412531}{2000000}}=\frac{2478968175}{-\frac{5255412531}{2000000}}$$

-\frac{5255412531}{2000000} ga bo'lish -\frac{5255412531}{2000000} ga ko'paytirishni bekor qiladi.

$$p^{2}+\frac{\frac{9221782491}{20000}}{-\frac{5255412531}{2000000}}p=\frac{2478968175}{-\frac{5255412531}{2000000}}$$

\frac{9221782491}{20000} ni -\frac{5255412531}{2000000} ga bo'lish \frac{9221782491}{20000} ga k'paytirish -\frac{5255412531}{2000000} ga qaytarish.

$$p^{2}-\frac{307392749700}{1751804177}p=\frac{2478968175}{-\frac{5255412531}{2000000}}$$

2478968175 ni -\frac{5255412531}{2000000} ga bo'lish 2478968175 ga k'paytirish -\frac{5255412531}{2000000} ga qaytarish.

$$p^{2}-\frac{307392749700}{1751804177}p=-\frac{50000000}{53}$$

-\frac{307392749700}{1751804177} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{153696374850}{1751804177} olish uchun. Keyin, -\frac{153696374850}{1751804177} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$p^{2}-\frac{307392749700}{1751804177}p+\left(-\frac{153696374850}{1751804177}\right)^{2}=-\frac{50000000}{53}+\left(-\frac{153696374850}{1751804177}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{153696374850}{1751804177} kvadratini chiqarish.

$$p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329}=-\frac{50000000}{53}+\frac{23622575642031712522500}{3068817874554647329}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{50000000}{53} ni \frac{23622575642031712522500}{3068817874554647329} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329}=-\frac{2871488626768012937477500}{3068817874554647329}$$

p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(p-\frac{153696374850}{1751804177}\right)^{2}=-\frac{2871488626768012937477500}{3068817874554647329}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(p-\frac{153696374850}{1751804177}\right)^{2}}=\sqrt{-\frac{2871488626768012937477500}{3068817874554647329}}$$

Qisqartirish.

$$p-\frac{153696374850}{1751804177}=\frac{50\sqrt{1148595450707205174991}i}{1751804177} p-\frac{153696374850}{1751804177}=-\frac{50\sqrt{1148595450707205174991}i}{1751804177}$$

\frac{153696374850}{1751804177} ni tenglamaning ikkala tarafiga qo'shish.

$$p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177} p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177}$$