63*10^-5=(02+x)(x)/(012-x) eching

$$63 \times 10 ^ { - 5 } = \frac { ( 02 + x ) ( x ) } { ( 012 - x ) }$$

x uchun yechish

$$x=-\frac{63}{100000}=-0,00063$$

Faktorlash qadamlari

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

$$63\times 10^{-5}x=-\left(0\times 2+x\right)x$$

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

$$63\times \frac{1}{100000}x=-\left(0\times 2+x\right)x$$

\frac{63}{100000} hosil qilish uchun 63 va \frac{1}{100000} ni ko'paytirish.

$$\frac{63}{100000}x=-\left(0\times 2+x\right)x$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$\frac{63}{100000}x=-xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{63}{100000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{63}{100000}x+x^{2}=0$$

x omili.

$$x\left(\frac{63}{100000}+x\right)=0$$

Tenglamani yechish uchun x=0 va \frac{63}{100000}+x=0 ni yeching.

$$x=0 x=-\frac{63}{100000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{63}{100000}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$63\times 10^{-5}x=-\left(0\times 2+x\right)x$$

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

$$63\times \frac{1}{100000}x=-\left(0\times 2+x\right)x$$

\frac{63}{100000} hosil qilish uchun 63 va \frac{1}{100000} ni ko'paytirish.

$$\frac{63}{100000}x=-\left(0\times 2+x\right)x$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$\frac{63}{100000}x=-xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{63}{100000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{63}{100000}x+x^{2}=0$$

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.

$$x^{2}+\frac{63}{100000}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, \frac{63}{100000} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\frac{63}{100000}±\sqrt{\left(\frac{63}{100000}\right)^{2}}}{2}$$

\left(\frac{63}{100000}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\frac{63}{100000}±\frac{63}{100000}}{2}$$

x=\frac{-\frac{63}{100000}±\frac{63}{100000}}{2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{63}{100000} ni \frac{63}{100000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

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

0 ni 2 ga bo'lish.

$$x=0$$

x=\frac{-\frac{63}{100000}±\frac{63}{100000}}{2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{63}{100000} ni -\frac{63}{100000} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=-\frac{\frac{63}{50000}}{2}$$

-\frac{63}{50000} ni 2 ga bo'lish.

$$x=-\frac{63}{100000}$$

Tenglama yechildi.

$$x=0 x=-\frac{63}{100000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{63}{100000}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$63\times 10^{-5}x=-\left(0\times 2+x\right)x$$

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

$$63\times \frac{1}{100000}x=-\left(0\times 2+x\right)x$$

\frac{63}{100000} hosil qilish uchun 63 va \frac{1}{100000} ni ko'paytirish.

$$\frac{63}{100000}x=-\left(0\times 2+x\right)x$$

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$\frac{63}{100000}x=-xx$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{63}{100000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{63}{100000}x+x^{2}=0$$

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

$$x^{2}+\frac{63}{100000}x=0$$

\frac{63}{100000} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{63}{200000} olish uchun. Keyin, \frac{63}{200000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{63}{100000}x+\left(\frac{63}{200000}\right)^{2}=\left(\frac{63}{200000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{63}{200000} kvadratini chiqarish.

$$x^{2}+\frac{63}{100000}x+\frac{3969}{40000000000}=\frac{3969}{40000000000}$$

x^{2}+\frac{63}{100000}x+\frac{3969}{40000000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{63}{200000}\right)^{2}=\frac{3969}{40000000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{63}{200000}\right)^{2}}=\sqrt{\frac{3969}{40000000000}}$$

Qisqartirish.

$$x+\frac{63}{200000}=\frac{63}{200000} x+\frac{63}{200000}=-\frac{63}{200000}$$

Tenglamaning ikkala tarafidan \frac{63}{200000} ni ayirish.

$$x=0 x=-\frac{63}{100000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{63}{100000}$$