3n^2=9n eching

$$3 n ^ { 2 } = 9 n$$

n uchun yechish

$$n=3$$

$$n=0$$

Faktorlash qadamlari

Ikkala tarafdan 9n ni ayirish.

$$3n^{2}-9n=0$$

n omili.

$$n\left(3n-9\right)=0$$

Tenglamani yechish uchun n=0 va 3n-9=0 ni yeching.

$$n=0 n=3$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 9n ni ayirish.

$$3n^{2}-9n=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -9 ni b va 0 ni c bilan almashtiring.

$$n=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2\times 3}$$

\left(-9\right)^{2} ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-9\right)±9}{2\times 3}$$

-9 ning teskarisi 9 ga teng.

$$n=\frac{9±9}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$n=\frac{9±9}{6}$$

n=\frac{9±9}{6} tenglamasini yeching, bunda ± musbat. 9 ni 9 ga qo'shish.

$$n=\frac{18}{6}$$

18 ni 6 ga bo'lish.

$$n=3$$

n=\frac{9±9}{6} tenglamasini yeching, bunda ± manfiy. 9 dan 9 ni ayirish.

$$n=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$n=0$$

Tenglama yechildi.

$$n=3 n=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 9n ni ayirish.

$$3n^{2}-9n=0$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3n^{2}-9n}{3}=\frac{0}{3}$$

3 ga bo'lish 3 ga ko'paytirishni bekor qiladi.

$$n^{2}+\left(-\frac{9}{3}\right)n=\frac{0}{3}$$

-9 ni 3 ga bo'lish.

$$n^{2}-3n=\frac{0}{3}$$

0 ni 3 ga bo'lish.

$$n^{2}-3n=0$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$n^{2}-3n+\frac{9}{4}=\frac{9}{4}$$

n^{2}-3n+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(n-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(n-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Qisqartirish.

$$n-\frac{3}{2}=\frac{3}{2} n-\frac{3}{2}=-\frac{3}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$n=3 n=0$$