x^2/308-x=83176*10^-5 eching

$$\frac{ { x }^{ 2 } }{ 308-x } = 83176 \times { 10 }^{ -5 }$$

x uchun yechish

$$x = \frac{\sqrt{160221897609} - 10397}{25000} \approx 15,595211036$$

$$x=\frac{-\sqrt{160221897609}-10397}{25000}\approx -16,426971036$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 308 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+308 ga ko'paytirish.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

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

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

\frac{10397}{12500} hosil qilish uchun 83176 va \frac{1}{100000} ni ko'paytirish.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

\frac{10397}{12500} ga -x+308 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

\frac{10397}{12500}x ni ikki tarafga qo’shing.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

Ikkala tarafdan \frac{800569}{3125} ni ayirish.

$$x^{2}+\frac{10397}{12500}x-\frac{800569}{3125}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, \frac{10397}{12500} ni b va -\frac{800569}{3125} ni c bilan almashtiring.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\left(\frac{10397}{12500}\right)^{2}-4\left(-\frac{800569}{3125}\right)}}{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{10397}{12500} kvadratini chiqarish.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}-4\left(-\frac{800569}{3125}\right)}}{2}$$

-4 ni -\frac{800569}{3125} marotabaga ko'paytirish.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}+\frac{3202276}{3125}}}{2}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{108097609}{156250000} ni \frac{3202276}{3125} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{160221897609}{156250000}}}{2}$$

\frac{160221897609}{156250000} ning kvadrat ildizini chiqarish.

$$x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2}$$

x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} tenglamasini yeching, bunda ± musbat. -\frac{10397}{12500} ni \frac{\sqrt{160221897609}}{12500} ga qo'shish.

$$x=\frac{\sqrt{160221897609}-10397}{2\times 12500}$$

\frac{-10397+\sqrt{160221897609}}{12500} ni 2 ga bo'lish.

$$x=\frac{\sqrt{160221897609}-10397}{25000}$$

x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} tenglamasini yeching, bunda ± manfiy. -\frac{10397}{12500} dan \frac{\sqrt{160221897609}}{12500} ni ayirish.

$$x=\frac{-\sqrt{160221897609}-10397}{2\times 12500}$$

\frac{-10397-\sqrt{160221897609}}{12500} ni 2 ga bo'lish.

$$x=\frac{-\sqrt{160221897609}-10397}{25000}$$

Tenglama yechildi.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 308 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini -x+308 ga ko'paytirish.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

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

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

\frac{10397}{12500} hosil qilish uchun 83176 va \frac{1}{100000} ni ko'paytirish.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

\frac{10397}{12500} ga -x+308 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

\frac{10397}{12500}x ni ikki tarafga qo’shing.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

\frac{10397}{12500} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{10397}{25000} olish uchun. Keyin, \frac{10397}{25000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{10397}{12500}x+\left(\frac{10397}{25000}\right)^{2}=\frac{800569}{3125}+\left(\frac{10397}{25000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{10397}{25000} kvadratini chiqarish.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{800569}{3125}+\frac{108097609}{625000000}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{800569}{3125} ni \frac{108097609}{625000000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{160221897609}{625000000}$$

x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{10397}{25000}\right)^{2}=\frac{160221897609}{625000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{10397}{25000}\right)^{2}}=\sqrt{\frac{160221897609}{625000000}}$$

Qisqartirish.

$$x+\frac{10397}{25000}=\frac{\sqrt{160221897609}}{25000} x+\frac{10397}{25000}=-\frac{\sqrt{160221897609}}{25000}$$

Tenglamaning ikkala tarafidan \frac{10397}{25000} ni ayirish.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$