3m(2m+9)=0 eching

$$3 m ( 2 m + 9 ) = 0$$

m uchun yechish

$$m = -\frac{9}{2} = -4\frac{1}{2} = -4,5$$

$$m=0$$

Faktorlash qadamlari

3m ga 2m+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6m^{2}+27m=0$$

m omili.

$$m\left(6m+27\right)=0$$

Tenglamani yechish uchun m=0 va 6m+27=0 ni yeching.

$$m=0 m=-\frac{9}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

3m ga 2m+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6m^{2}+27m=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, 27 ni b va 0 ni c bilan almashtiring.

$$m=\frac{-27±\sqrt{27^{2}}}{2\times 6}$$

27^{2} ning kvadrat ildizini chiqarish.

$$m=\frac{-27±27}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$m=\frac{-27±27}{12}$$

m=\frac{-27±27}{12} tenglamasini yeching, bunda ± musbat. -27 ni 27 ga qo'shish.

$$m=\frac{0}{12}$$

0 ni 12 ga bo'lish.

$$m=0$$

m=\frac{-27±27}{12} tenglamasini yeching, bunda ± manfiy. -27 dan 27 ni ayirish.

$$m=-\frac{54}{12}$$

\frac{-54}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$m=-\frac{9}{2}$$

Tenglama yechildi.

$$m=0 m=-\frac{9}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

3m ga 2m+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6m^{2}+27m=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6m^{2}+27m}{6}=\frac{0}{6}$$

6 ga bo'lish 6 ga ko'paytirishni bekor qiladi.

$$m^{2}+\frac{27}{6}m=\frac{0}{6}$$

\frac{27}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$m^{2}+\frac{9}{2}m=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$m^{2}+\frac{9}{2}m=0$$

\frac{9}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga \frac{9}{4} olish uchun. Keyin, \frac{9}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$m^{2}+\frac{9}{2}m+\left(\frac{9}{4}\right)^{2}=\left(\frac{9}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib \frac{9}{4} kvadratini chiqarish.

$$m^{2}+\frac{9}{2}m+\frac{81}{16}=\frac{81}{16}$$

m^{2}+\frac{9}{2}m+\frac{81}{16} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(m+\frac{9}{4}\right)^{2}=\frac{81}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(m+\frac{9}{4}\right)^{2}}=\sqrt{\frac{81}{16}}$$

Qisqartirish.

$$m+\frac{9}{4}=\frac{9}{4} m+\frac{9}{4}=-\frac{9}{4}$$

Tenglamaning ikkala tarafidan \frac{9}{4} ni ayirish.

$$m=0 m=-\frac{9}{2}$$