1410^-4=(00107+x)x/00758-x eching

$$14 { 10 }^{ -4 } = \frac{ (00107+x)x }{ 00758-x }$$

x uchun yechish

$$x=-\frac{7}{5000}=-0,0014$$

Faktorlash qadamlari

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

$$14\times 10^{-4}x=-\left(0\times 0\times 107+x\right)x$$

-4 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000} ni qiymatni oling.

$$14\times \frac{1}{10000}x=-\left(0\times 0\times 107+x\right)x$$

\frac{7}{5000} hosil qilish uchun 14 va \frac{1}{10000} ni ko'paytirish.

$$\frac{7}{5000}x=-\left(0\times 0\times 107+x\right)x$$

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

$$\frac{7}{5000}x=-\left(0\times 107+x\right)x$$

0 hosil qilish uchun 0 va 107 ni ko'paytirish.

$$\frac{7}{5000}x=-xx$$

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

$$\frac{7}{5000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{7}{5000}x+x^{2}=0$$

x omili.

$$x\left(\frac{7}{5000}+x\right)=0$$

Tenglamani yechish uchun x=0 va \frac{7}{5000}+x=0 ni yeching.

$$x=0 x=-\frac{7}{5000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{7}{5000}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$14\times 10^{-4}x=-\left(0\times 0\times 107+x\right)x$$

-4 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000} ni qiymatni oling.

$$14\times \frac{1}{10000}x=-\left(0\times 0\times 107+x\right)x$$

\frac{7}{5000} hosil qilish uchun 14 va \frac{1}{10000} ni ko'paytirish.

$$\frac{7}{5000}x=-\left(0\times 0\times 107+x\right)x$$

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

$$\frac{7}{5000}x=-\left(0\times 107+x\right)x$$

0 hosil qilish uchun 0 va 107 ni ko'paytirish.

$$\frac{7}{5000}x=-xx$$

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

$$\frac{7}{5000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{7}{5000}x+x^{2}=0$$

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.

$$x^{2}+\frac{7}{5000}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, \frac{7}{5000} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\frac{7}{5000}±\sqrt{\left(\frac{7}{5000}\right)^{2}}}{2}$$

\left(\frac{7}{5000}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\frac{7}{5000}±\frac{7}{5000}}{2}$$

x=\frac{-\frac{7}{5000}±\frac{7}{5000}}{2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{7}{5000} ni \frac{7}{5000} 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{7}{5000}±\frac{7}{5000}}{2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{7}{5000} ni -\frac{7}{5000} dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$x=-\frac{\frac{7}{2500}}{2}$$

-\frac{7}{2500} ni 2 ga bo'lish.

$$x=-\frac{7}{5000}$$

Tenglama yechildi.

$$x=0 x=-\frac{7}{5000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{7}{5000}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$14\times 10^{-4}x=-\left(0\times 0\times 107+x\right)x$$

-4 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{10000} ni qiymatni oling.

$$14\times \frac{1}{10000}x=-\left(0\times 0\times 107+x\right)x$$

\frac{7}{5000} hosil qilish uchun 14 va \frac{1}{10000} ni ko'paytirish.

$$\frac{7}{5000}x=-\left(0\times 0\times 107+x\right)x$$

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

$$\frac{7}{5000}x=-\left(0\times 107+x\right)x$$

0 hosil qilish uchun 0 va 107 ni ko'paytirish.

$$\frac{7}{5000}x=-xx$$

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

$$\frac{7}{5000}x=-x^{2}$$

x^{2} ni ikki tarafga qo’shing.

$$\frac{7}{5000}x+x^{2}=0$$

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

$$x^{2}+\frac{7}{5000}x=0$$

\frac{7}{5000} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{7}{10000} olish uchun. Keyin, \frac{7}{10000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{7}{5000}x+\left(\frac{7}{10000}\right)^{2}=\left(\frac{7}{10000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{7}{10000} kvadratini chiqarish.

$$x^{2}+\frac{7}{5000}x+\frac{49}{100000000}=\frac{49}{100000000}$$

x^{2}+\frac{7}{5000}x+\frac{49}{100000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{7}{10000}\right)^{2}=\frac{49}{100000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{7}{10000}\right)^{2}}=\sqrt{\frac{49}{100000000}}$$

Qisqartirish.

$$x+\frac{7}{10000}=\frac{7}{10000} x+\frac{7}{10000}=-\frac{7}{10000}$$

Tenglamaning ikkala tarafidan \frac{7}{10000} ni ayirish.

$$x=0 x=-\frac{7}{5000}$$

x qiymati 0 teng bo‘lmaydi.

$$x=-\frac{7}{5000}$$