64+(n-1)*2/n*n=858 eching

$$\frac { 64 + ( n - 1 ) \cdot 2 } { n } \cdot n = 858$$

n uchun yechish

$$n=398$$

Faktorlash qadamlari

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

$$\left(64+\left(n-1\right)\times 2\right)n=858n$$

n-1 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(64+2n-2\right)n=858n$$

62 olish uchun 64 dan 2 ni ayirish.

$$\left(62+2n\right)n=858n$$

62+2n ga n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$62n+2n^{2}=858n$$

Ikkala tarafdan 858n ni ayirish.

$$62n+2n^{2}-858n=0$$

-796n ni olish uchun 62n va -858n ni birlashtirish.

$$-796n+2n^{2}=0$$

n omili.

$$n\left(-796+2n\right)=0$$

Tenglamani yechish uchun n=0 va -796+2n=0 ni yeching.

$$n=0 n=398$$

n qiymati 0 teng bo‘lmaydi.

$$n=398$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$\left(64+\left(n-1\right)\times 2\right)n=858n$$

n-1 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(64+2n-2\right)n=858n$$

62 olish uchun 64 dan 2 ni ayirish.

$$\left(62+2n\right)n=858n$$

62+2n ga n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$62n+2n^{2}=858n$$

Ikkala tarafdan 858n ni ayirish.

$$62n+2n^{2}-858n=0$$

-796n ni olish uchun 62n va -858n ni birlashtirish.

$$-796n+2n^{2}=0$$

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.

$$2n^{2}-796n=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, -796 ni b va 0 ni c bilan almashtiring.

$$n=\frac{-\left(-796\right)±\sqrt{\left(-796\right)^{2}}}{2\times 2}$$

\left(-796\right)^{2} ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-796\right)±796}{2\times 2}$$

-796 ning teskarisi 796 ga teng.

$$n=\frac{796±796}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$n=\frac{796±796}{4}$$

n=\frac{796±796}{4} tenglamasini yeching, bunda ± musbat. 796 ni 796 ga qo'shish.

$$n=\frac{1592}{4}$$

1592 ni 4 ga bo'lish.

$$n=398$$

n=\frac{796±796}{4} tenglamasini yeching, bunda ± manfiy. 796 dan 796 ni ayirish.

$$n=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$n=0$$

Tenglama yechildi.

$$n=398 n=0$$

n qiymati 0 teng bo‘lmaydi.

$$n=398$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$\left(64+\left(n-1\right)\times 2\right)n=858n$$

n-1 ga 2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(64+2n-2\right)n=858n$$

62 olish uchun 64 dan 2 ni ayirish.

$$\left(62+2n\right)n=858n$$

62+2n ga n ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$62n+2n^{2}=858n$$

Ikkala tarafdan 858n ni ayirish.

$$62n+2n^{2}-858n=0$$

-796n ni olish uchun 62n va -858n ni birlashtirish.

$$-796n+2n^{2}=0$$

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

$$2n^{2}-796n=0$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2n^{2}-796n}{2}=\frac{0}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$n^{2}+\left(-\frac{796}{2}\right)n=\frac{0}{2}$$

-796 ni 2 ga bo'lish.

$$n^{2}-398n=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$n^{2}-398n=0$$

-398 ni bo‘lish, x shartining koeffitsienti, 2 ga -199 olish uchun. Keyin, -199 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-398n+\left(-199\right)^{2}=\left(-199\right)^{2}$$

-199 kvadratini chiqarish.

$$n^{2}-398n+39601=39601$$

n^{2}-398n+39601 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n-199\right)^{2}=39601$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-199\right)^{2}}=\sqrt{39601}$$

Qisqartirish.

$$n-199=199 n-199=-199$$

199 ni tenglamaning ikkala tarafiga qo'shish.

$$n=398 n=0$$

n qiymati 0 teng bo‘lmaydi.

$$n=398$$