9(x^2)=3x eching

$$9 ( x ^ { 2 } ) = 3 x$$

x uchun yechish

$$x=\frac{1}{3}\approx 0,333333333$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 3x ni ayirish.

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

x omili.

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

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

$$x=0 x=\frac{1}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 3x ni ayirish.

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

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

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

\left(-3\right)^{2} ning kvadrat ildizini chiqarish.

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

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±3}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{3±3}{18}$$

x=\frac{3±3}{18} tenglamasini yeching, bunda ± musbat. 3 ni 3 ga qo'shish.

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

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

$$x=\frac{1}{3}$$

x=\frac{3±3}{18} tenglamasini yeching, bunda ± manfiy. 3 dan 3 ni ayirish.

$$x=\frac{0}{18}$$

0 ni 18 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{1}{3} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 3x ni ayirish.

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

Ikki tarafini 9 ga bo‘ling.

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

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

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

\frac{-3}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{1}{3}x=\frac{0}{9}$$

0 ni 9 ga bo'lish.

$$x^{2}-\frac{1}{3}x=0$$

-\frac{1}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{6} olish uchun. Keyin, -\frac{1}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{1}{3}x+\left(-\frac{1}{6}\right)^{2}=\left(-\frac{1}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{6} kvadratini chiqarish.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{1}{36}$$

x^{2}-\frac{1}{3}x+\frac{1}{36} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{1}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{1}{36}}$$

Qisqartirish.

$$x-\frac{1}{6}=\frac{1}{6} x-\frac{1}{6}=-\frac{1}{6}$$

\frac{1}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{1}{3} x=0$$