n(9n+10)+4=0 eching

$$n ( 9 n + 10 ) + 4 = 0$$

n uchun yechish

$$n=\frac{-5+\sqrt{11}i}{9}\approx -0,555555556+0,368513866i$$

$$n=\frac{-\sqrt{11}i-5}{9}\approx -0,555555556-0,368513866i$$

Kvadrat tenglamalaridan foydalanish qoidalari

n ga 9n+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9n^{2}+10n+4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 9 ni a, 10 ni b va 4 ni c bilan almashtiring.

$$n=\frac{-10±\sqrt{10^{2}-4\times 9\times 4}}{2\times 9}$$

10 kvadratini chiqarish.

$$n=\frac{-10±\sqrt{100-4\times 9\times 4}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$n=\frac{-10±\sqrt{100-36\times 4}}{2\times 9}$$

-36 ni 4 marotabaga ko'paytirish.

$$n=\frac{-10±\sqrt{100-144}}{2\times 9}$$

100 ni -144 ga qo'shish.

$$n=\frac{-10±\sqrt{-44}}{2\times 9}$$

-44 ning kvadrat ildizini chiqarish.

$$n=\frac{-10±2\sqrt{11}i}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$n=\frac{-10±2\sqrt{11}i}{18}$$

n=\frac{-10±2\sqrt{11}i}{18} tenglamasini yeching, bunda ± musbat. -10 ni 2i\sqrt{11} ga qo'shish.

$$n=\frac{-10+2\sqrt{11}i}{18}$$

-10+2i\sqrt{11} ni 18 ga bo'lish.

$$n=\frac{-5+\sqrt{11}i}{9}$$

n=\frac{-10±2\sqrt{11}i}{18} tenglamasini yeching, bunda ± manfiy. -10 dan 2i\sqrt{11} ni ayirish.

$$n=\frac{-2\sqrt{11}i-10}{18}$$

-10-2i\sqrt{11} ni 18 ga bo'lish.

$$n=\frac{-\sqrt{11}i-5}{9}$$

Tenglama yechildi.

$$n=\frac{-5+\sqrt{11}i}{9} n=\frac{-\sqrt{11}i-5}{9}$$

Kvadratni yakunlash bo'yicha qadamlar

n ga 9n+10 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9n^{2}+10n+4=0$$

Ikkala tarafdan 4 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$9n^{2}+10n=-4$$

Ikki tarafini 9 ga bo‘ling.

$$\frac{9n^{2}+10n}{9}=-\frac{4}{9}$$

9 ga bo'lish 9 ga ko'paytirishni bekor qiladi.

$$n^{2}+\frac{10}{9}n=-\frac{4}{9}$$

\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.

$$n^{2}+\frac{10}{9}n+\left(\frac{5}{9}\right)^{2}=-\frac{4}{9}+\left(\frac{5}{9}\right)^{2}$$

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

$$n^{2}+\frac{10}{9}n+\frac{25}{81}=-\frac{4}{9}+\frac{25}{81}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{4}{9} ni \frac{25}{81} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$n^{2}+\frac{10}{9}n+\frac{25}{81}=-\frac{11}{81}$$

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.

$$\left(n+\frac{5}{9}\right)^{2}=-\frac{11}{81}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n+\frac{5}{9}\right)^{2}}=\sqrt{-\frac{11}{81}}$$

Qisqartirish.

$$n+\frac{5}{9}=\frac{\sqrt{11}i}{9} n+\frac{5}{9}=-\frac{\sqrt{11}i}{9}$$

Tenglamaning ikkala tarafidan \frac{5}{9} ni ayirish.

$$n=\frac{-5+\sqrt{11}i}{9} n=\frac{-\sqrt{11}i-5}{9}$$