x^2/0*2-x=1810^-5 eching

$$\frac{ { x }^{ 2 } }{ 0 \cdot 2-x } = 18 { 10 }^{ -5 }$$

x uchun yechish

$$x=-\frac{9}{50000}=-0,00018$$

Faktorlash qadamlari

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

$$-x^{2}=18\times 10^{-5}x$$

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

$$-x^{2}=18\times \frac{1}{100000}x$$

\frac{9}{50000} hosil qilish uchun 18 va \frac{1}{100000} ni ko'paytirish.

$$-x^{2}=\frac{9}{50000}x$$

Ikkala tarafdan \frac{9}{50000}x ni ayirish.

$$-x^{2}-\frac{9}{50000}x=0$$

x omili.

$$x\left(-x-\frac{9}{50000}\right)=0$$

Tenglamani yechish uchun x=0 va -x-\frac{9}{50000}=0 ni yeching.

$$x=0 x=-\frac{9}{50000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{9}{50000}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$-x^{2}=18\times 10^{-5}x$$

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

$$-x^{2}=18\times \frac{1}{100000}x$$

\frac{9}{50000} hosil qilish uchun 18 va \frac{1}{100000} ni ko'paytirish.

$$-x^{2}=\frac{9}{50000}x$$

Ikkala tarafdan \frac{9}{50000}x ni ayirish.

$$-x^{2}-\frac{9}{50000}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -\frac{9}{50000} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{9}{50000}\right)±\sqrt{\left(-\frac{9}{50000}\right)^{2}}}{2\left(-1\right)}$$

\left(-\frac{9}{50000}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{9}{50000}\right)±\frac{9}{50000}}{2\left(-1\right)}$$

-\frac{9}{50000} ning teskarisi \frac{9}{50000} ga teng.

$$x=\frac{\frac{9}{50000}±\frac{9}{50000}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{\frac{9}{50000}±\frac{9}{50000}}{-2}$$

x=\frac{\frac{9}{50000}±\frac{9}{50000}}{-2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{9}{50000} ni \frac{9}{50000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{\frac{9}{25000}}{-2}$$

\frac{9}{25000} ni -2 ga bo'lish.

$$x=-\frac{9}{50000}$$

x=\frac{\frac{9}{50000}±\frac{9}{50000}}{-2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{9}{50000} ni \frac{9}{50000} 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.

$$x=-\frac{9}{50000} x=0$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{9}{50000}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$-x^{2}=18\times 10^{-5}x$$

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

$$-x^{2}=18\times \frac{1}{100000}x$$

\frac{9}{50000} hosil qilish uchun 18 va \frac{1}{100000} ni ko'paytirish.

$$-x^{2}=\frac{9}{50000}x$$

Ikkala tarafdan \frac{9}{50000}x ni ayirish.

$$-x^{2}-\frac{9}{50000}x=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-\frac{9}{50000}x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\left(-\frac{\frac{9}{50000}}{-1}\right)x=\frac{0}{-1}$$

-\frac{9}{50000} ni -1 ga bo'lish.

$$x^{2}+\frac{9}{50000}x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$x^{2}+\frac{9}{50000}x=0$$

\frac{9}{50000} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{9}{100000} olish uchun. Keyin, \frac{9}{100000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{9}{50000}x+\left(\frac{9}{100000}\right)^{2}=\left(\frac{9}{100000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9}{100000} kvadratini chiqarish.

$$x^{2}+\frac{9}{50000}x+\frac{81}{10000000000}=\frac{81}{10000000000}$$

x^{2}+\frac{9}{50000}x+\frac{81}{10000000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{9}{100000}\right)^{2}=\frac{81}{10000000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{9}{100000}\right)^{2}}=\sqrt{\frac{81}{10000000000}}$$

Qisqartirish.

$$x+\frac{9}{100000}=\frac{9}{100000} x+\frac{9}{100000}=-\frac{9}{100000}$$

Tenglamaning ikkala tarafidan \frac{9}{100000} ni ayirish.

$$x=0 x=-\frac{9}{50000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{9}{50000}$$