-48=n/2(2(9)(n-1)-2) eching

$$- 48 = \frac { n } { 2 } ( 2 ( 9 ) ( n - 1 ) - 2 )$$

n uchun yechish

$$n=\frac{5+\sqrt{407}i}{9}\approx 0,555555556+2,241582334i$$

$$n=\frac{-\sqrt{407}i+5}{9}\approx 0,555555556-2,241582334i$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$-96=n\left(2\times 9\left(n-1\right)-2\right)$$

18 hosil qilish uchun 2 va 9 ni ko'paytirish.

$$-96=n\left(18\left(n-1\right)-2\right)$$

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

$$-96=n\left(18n-18-2\right)$$

-20 olish uchun -18 dan 2 ni ayirish.

$$-96=n\left(18n-20\right)$$

n ga 18n-20 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-96=18n^{2}-20n$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$18n^{2}-20n=-96$$

96 ni ikki tarafga qo’shing.

$$18n^{2}-20n+96=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 18 ni a, -20 ni b va 96 ni c bilan almashtiring.

$$n=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 18\times 96}}{2\times 18}$$

-20 kvadratini chiqarish.

$$n=\frac{-\left(-20\right)±\sqrt{400-4\times 18\times 96}}{2\times 18}$$

-4 ni 18 marotabaga ko'paytirish.

$$n=\frac{-\left(-20\right)±\sqrt{400-72\times 96}}{2\times 18}$$

-72 ni 96 marotabaga ko'paytirish.

$$n=\frac{-\left(-20\right)±\sqrt{400-6912}}{2\times 18}$$

400 ni -6912 ga qo'shish.

$$n=\frac{-\left(-20\right)±\sqrt{-6512}}{2\times 18}$$

-6512 ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-20\right)±4\sqrt{407}i}{2\times 18}$$

-20 ning teskarisi 20 ga teng.

$$n=\frac{20±4\sqrt{407}i}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$n=\frac{20±4\sqrt{407}i}{36}$$

n=\frac{20±4\sqrt{407}i}{36} tenglamasini yeching, bunda ± musbat. 20 ni 4i\sqrt{407} ga qo'shish.

$$n=\frac{20+4\sqrt{407}i}{36}$$

20+4i\sqrt{407} ni 36 ga bo'lish.

$$n=\frac{5+\sqrt{407}i}{9}$$

n=\frac{20±4\sqrt{407}i}{36} tenglamasini yeching, bunda ± manfiy. 20 dan 4i\sqrt{407} ni ayirish.

$$n=\frac{-4\sqrt{407}i+20}{36}$$

20-4i\sqrt{407} ni 36 ga bo'lish.

$$n=\frac{-\sqrt{407}i+5}{9}$$

Tenglama yechildi.

$$n=\frac{5+\sqrt{407}i}{9} n=\frac{-\sqrt{407}i+5}{9}$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini 2 ga ko'paytirish.

$$-96=n\left(2\times 9\left(n-1\right)-2\right)$$

18 hosil qilish uchun 2 va 9 ni ko'paytirish.

$$-96=n\left(18\left(n-1\right)-2\right)$$

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

$$-96=n\left(18n-18-2\right)$$

-20 olish uchun -18 dan 2 ni ayirish.

$$-96=n\left(18n-20\right)$$

n ga 18n-20 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-96=18n^{2}-20n$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$18n^{2}-20n=-96$$

Ikki tarafini 18 ga bo‘ling.

$$\frac{18n^{2}-20n}{18}=-\frac{96}{18}$$

18 ga bo'lish 18 ga ko'paytirishni bekor qiladi.

$$n^{2}+\left(-\frac{20}{18}\right)n=-\frac{96}{18}$$

\frac{-20}{18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$n^{2}-\frac{10}{9}n=-\frac{96}{18}$$

\frac{-96}{18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$n^{2}-\frac{10}{9}n=-\frac{16}{3}$$

-\frac{10}{9} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{9} olish uchun. Keyin, -\frac{5}{9} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$n^{2}-\frac{10}{9}n+\left(-\frac{5}{9}\right)^{2}=-\frac{16}{3}+\left(-\frac{5}{9}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{9} kvadratini chiqarish.

$$n^{2}-\frac{10}{9}n+\frac{25}{81}=-\frac{16}{3}+\frac{25}{81}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{16}{3} ni \frac{25}{81} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$n^{2}-\frac{10}{9}n+\frac{25}{81}=-\frac{407}{81}$$

n^{2}-\frac{10}{9}n+\frac{25}{81} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n-\frac{5}{9}\right)^{2}=-\frac{407}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{5}{9}\right)^{2}}=\sqrt{-\frac{407}{81}}$$

Qisqartirish.

$$n-\frac{5}{9}=\frac{\sqrt{407}i}{9} n-\frac{5}{9}=-\frac{\sqrt{407}i}{9}$$

\frac{5}{9} ni tenglamaning ikkala tarafiga qo'shish.

$$n=\frac{5+\sqrt{407}i}{9} n=\frac{-\sqrt{407}i+5}{9}$$