x^2/035-x=83176*10^-5 eching

$$\frac{ { x }^{ 2 } }{ 035-x } = 83176 \times { 10 }^{ -5 }$$

x uchun yechish

$$x=-\frac{10397}{12500}=-0,83176$$

Faktorlash qadamlari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

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

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

$$-x^{2}=83176\times \frac{1}{100000}x$$

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

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

Ikkala tarafdan \frac{10397}{12500}x ni ayirish.

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

x omili.

$$x\left(-x-\frac{10397}{12500}\right)=0$$

Tenglamani yechish uchun x=0 va -x-\frac{10397}{12500}=0 ni yeching.

$$x=0 x=-\frac{10397}{12500}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{10397}{12500}$$

Kvadrat tenglamalaridan foydalanish qoidalari

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

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

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

$$-x^{2}=83176\times \frac{1}{100000}x$$

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

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

Ikkala tarafdan \frac{10397}{12500}x ni ayirish.

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

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 0 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{10397}{12500}\right)±\sqrt{\left(-\frac{10397}{12500}\right)^{2}}}{2\left(-1\right)}$$

\left(-\frac{10397}{12500}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{10397}{12500}\right)±\frac{10397}{12500}}{2\left(-1\right)}$$

-\frac{10397}{12500} ning teskarisi \frac{10397}{12500} ga teng.

$$x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

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

x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{-2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{10397}{12500} ni \frac{10397}{12500} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{\frac{10397}{6250}}{-2}$$

\frac{10397}{6250} ni -2 ga bo'lish.

$$x=-\frac{10397}{12500}$$

x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{-2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{10397}{12500} ni \frac{10397}{12500} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-\frac{10397}{12500} x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{10397}{12500}$$

Kvadratni yakunlash bo'yicha qadamlar

x qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini x ga ko'paytirish.

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

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

$$-x^{2}=83176\times \frac{1}{100000}x$$

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

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

Ikkala tarafdan \frac{10397}{12500}x ni ayirish.

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

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-\frac{10397}{12500}x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\left(-\frac{\frac{10397}{12500}}{-1}\right)x=\frac{0}{-1}$$

-\frac{10397}{12500} ni -1 ga bo'lish.

$$x^{2}+\frac{10397}{12500}x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

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

\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.

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

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

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

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.

$$\left(x+\frac{10397}{25000}\right)^{2}=\frac{108097609}{625000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{10397}{25000}\right)^{2}}=\sqrt{\frac{108097609}{625000000}}$$

Qisqartirish.

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

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

$$x=0 x=-\frac{10397}{12500}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{10397}{12500}$$