174*10^-5=x^2/00100-x eching

$$174 \times { 10 }^{ -5 } = \frac{ { x }^{ 2 } }{ 00100-x }$$

x uchun yechish

$$x=-\frac{87}{50000}=-0,00174$$

Faktorlash qadamlari

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

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

\frac{87}{50000} hosil qilish uchun 174 va \frac{1}{100000} ni ko'paytirish.

$$\frac{87}{50000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{87}{50000}x+x^{2}=0$$

x omili.

$$x\left(\frac{87}{50000}+x\right)=0$$

Tenglamani yechish uchun x=0 va \frac{87}{50000}+x=0 ni yeching.

$$x=0 x=-\frac{87}{50000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{87}{50000}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

\frac{87}{50000} hosil qilish uchun 174 va \frac{1}{100000} ni ko'paytirish.

$$\frac{87}{50000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{87}{50000}x+x^{2}=0$$

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.

$$x^{2}+\frac{87}{50000}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, \frac{87}{50000} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\frac{87}{50000}±\sqrt{\left(\frac{87}{50000}\right)^{2}}}{2}$$

\left(\frac{87}{50000}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2}$$

x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{87}{50000} ni \frac{87}{50000} 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{87}{50000}±\frac{87}{50000}}{2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{87}{50000} ni -\frac{87}{50000} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=-\frac{\frac{87}{25000}}{2}$$

-\frac{87}{25000} ni 2 ga bo'lish.

$$x=-\frac{87}{50000}$$

Tenglama yechildi.

$$x=0 x=-\frac{87}{50000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{87}{50000}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

\frac{87}{50000} hosil qilish uchun 174 va \frac{1}{100000} ni ko'paytirish.

$$\frac{87}{50000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{87}{50000}x+x^{2}=0$$

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

$$x^{2}+\frac{87}{50000}x=0$$

\frac{87}{50000} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{87}{100000} olish uchun. Keyin, \frac{87}{100000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{87}{50000}x+\left(\frac{87}{100000}\right)^{2}=\left(\frac{87}{100000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{87}{100000} kvadratini chiqarish.

$$x^{2}+\frac{87}{50000}x+\frac{7569}{10000000000}=\frac{7569}{10000000000}$$

x^{2}+\frac{87}{50000}x+\frac{7569}{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.

$$\left(x+\frac{87}{100000}\right)^{2}=\frac{7569}{10000000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{87}{100000}\right)^{2}}=\sqrt{\frac{7569}{10000000000}}$$

Qisqartirish.

$$x+\frac{87}{100000}=\frac{87}{100000} x+\frac{87}{100000}=-\frac{87}{100000}$$

Tenglamaning ikkala tarafidan \frac{87}{100000} ni ayirish.

$$x=0 x=-\frac{87}{50000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{87}{50000}$$