(2x)(3x-5)=0 eching

$$(2x)(3x-5)=0$$

x uchun yechish

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1,666666667$$

$$x=0$$

Faktorlash qadamlari

2x ga 3x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-10x=0$$

x omili.

$$x\left(6x-10\right)=0$$

Tenglamani yechish uchun x=0 va 6x-10=0 ni yeching.

$$x=0 x=\frac{5}{3}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga 3x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-10x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -10 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 6}$$

\left(-10\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-10\right)±10}{2\times 6}$$

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±10}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{10±10}{12}$$

x=\frac{10±10}{12} tenglamasini yeching, bunda ± musbat. 10 ni 10 ga qo'shish.

$$x=\frac{20}{12}$$

\frac{20}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{5}{3}$$

x=\frac{10±10}{12} tenglamasini yeching, bunda ± manfiy. 10 dan 10 ni ayirish.

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

0 ni 12 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{5}{3} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

2x ga 3x-5 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-10x=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-10x}{6}=\frac{0}{6}$$

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

$$x^{2}+\left(-\frac{10}{6}\right)x=\frac{0}{6}$$

\frac{-10}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{5}{3}x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x^{2}-\frac{5}{3}x=0$$

-\frac{5}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{6} olish uchun. Keyin, -\frac{5}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{5}{3}x+\left(-\frac{5}{6}\right)^{2}=\left(-\frac{5}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{6} kvadratini chiqarish.

$$x^{2}-\frac{5}{3}x+\frac{25}{36}=\frac{25}{36}$$

x^{2}-\frac{5}{3}x+\frac{25}{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.

$$\left(x-\frac{5}{6}\right)^{2}=\frac{25}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{5}{6}\right)^{2}}=\sqrt{\frac{25}{36}}$$

Qisqartirish.

$$x-\frac{5}{6}=\frac{5}{6} x-\frac{5}{6}=-\frac{5}{6}$$

\frac{5}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{5}{3} x=0$$