463*10^-3(0123-x)=x^2 eching

$$463 \times 10 ^ { - 3 } ( 0123 - x ) = x ^ { 2 }$$

x uchun yechish

$$x=-\frac{463}{1000}=-0,463$$

$$x=0$$

Faktorlash qadamlari

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$463\times \frac{1}{1000}\left(0\times 123-x\right)=x^{2}$$

\frac{463}{1000} hosil qilish uchun 463 va \frac{1}{1000} ni ko'paytirish.

$$\frac{463}{1000}\left(0\times 123-x\right)=x^{2}$$

0 hosil qilish uchun 0 va 123 ni ko'paytirish.

$$\frac{463}{1000}\left(0-x\right)=x^{2}$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{463}{1000}\left(-1\right)x=x^{2}$$

-\frac{463}{1000} hosil qilish uchun \frac{463}{1000} va -1 ni ko'paytirish.

$$-\frac{463}{1000}x=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-\frac{463}{1000}x-x^{2}=0$$

x omili.

$$x\left(-\frac{463}{1000}-x\right)=0$$

Tenglamani yechish uchun x=0 va -\frac{463}{1000}-x=0 ni yeching.

$$x=0 x=-\frac{463}{1000}$$

Kvadrat tenglamalaridan foydalanish qoidalari

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$463\times \frac{1}{1000}\left(0\times 123-x\right)=x^{2}$$

\frac{463}{1000} hosil qilish uchun 463 va \frac{1}{1000} ni ko'paytirish.

$$\frac{463}{1000}\left(0\times 123-x\right)=x^{2}$$

0 hosil qilish uchun 0 va 123 ni ko'paytirish.

$$\frac{463}{1000}\left(0-x\right)=x^{2}$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{463}{1000}\left(-1\right)x=x^{2}$$

-\frac{463}{1000} hosil qilish uchun \frac{463}{1000} va -1 ni ko'paytirish.

$$-\frac{463}{1000}x=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-\frac{463}{1000}x-x^{2}=0$$

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.

$$-x^{2}-\frac{463}{1000}x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -\frac{463}{1000} ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-\frac{463}{1000}\right)±\sqrt{\left(-\frac{463}{1000}\right)^{2}}}{2\left(-1\right)}$$

\left(-\frac{463}{1000}\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-\frac{463}{1000}\right)±\frac{463}{1000}}{2\left(-1\right)}$$

-\frac{463}{1000} ning teskarisi \frac{463}{1000} ga teng.

$$x=\frac{\frac{463}{1000}±\frac{463}{1000}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{\frac{463}{1000}±\frac{463}{1000}}{-2}$$

x=\frac{\frac{463}{1000}±\frac{463}{1000}}{-2} tenglamasini yeching, bunda ± musbat. Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{463}{1000} ni \frac{463}{1000} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x=\frac{\frac{463}{500}}{-2}$$

\frac{463}{500} ni -2 ga bo'lish.

$$x=-\frac{463}{1000}$$

x=\frac{\frac{463}{1000}±\frac{463}{1000}}{-2} tenglamasini yeching, bunda ± manfiy. Umumiy maxrajni topib va suratlarni ayirib \frac{463}{1000} ni \frac{463}{1000} 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.

$$x=-\frac{463}{1000} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

-3 daraja ko‘rsatkichini 10 ga hisoblang va \frac{1}{1000} ni qiymatni oling.

$$463\times \frac{1}{1000}\left(0\times 123-x\right)=x^{2}$$

\frac{463}{1000} hosil qilish uchun 463 va \frac{1}{1000} ni ko'paytirish.

$$\frac{463}{1000}\left(0\times 123-x\right)=x^{2}$$

0 hosil qilish uchun 0 va 123 ni ko'paytirish.

$$\frac{463}{1000}\left(0-x\right)=x^{2}$$

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$\frac{463}{1000}\left(-1\right)x=x^{2}$$

-\frac{463}{1000} hosil qilish uchun \frac{463}{1000} va -1 ni ko'paytirish.

$$-\frac{463}{1000}x=x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$-\frac{463}{1000}x-x^{2}=0$$

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

$$-x^{2}-\frac{463}{1000}x=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-\frac{463}{1000}x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\left(-\frac{\frac{463}{1000}}{-1}\right)x=\frac{0}{-1}$$

-\frac{463}{1000} ni -1 ga bo'lish.

$$x^{2}+\frac{463}{1000}x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$x^{2}+\frac{463}{1000}x=0$$

\frac{463}{1000} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{463}{2000} olish uchun. Keyin, \frac{463}{2000} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+\frac{463}{1000}x+\left(\frac{463}{2000}\right)^{2}=\left(\frac{463}{2000}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{463}{2000} kvadratini chiqarish.

$$x^{2}+\frac{463}{1000}x+\frac{214369}{4000000}=\frac{214369}{4000000}$$

x^{2}+\frac{463}{1000}x+\frac{214369}{4000000} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+\frac{463}{2000}\right)^{2}=\frac{214369}{4000000}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+\frac{463}{2000}\right)^{2}}=\sqrt{\frac{214369}{4000000}}$$

Qisqartirish.

$$x+\frac{463}{2000}=\frac{463}{2000} x+\frac{463}{2000}=-\frac{463}{2000}$$

Tenglamaning ikkala tarafidan \frac{463}{2000} ni ayirish.

$$x=0 x=-\frac{463}{1000}$$