2x(3x-4)=5x eching

$$2x(3x-4)=5x$$

x uchun yechish

$$x = \frac{13}{6} = 2\frac{1}{6} \approx 2,166666667$$

$$x=0$$

Faktorlash qadamlari

2x ga 3x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-8x=5x$$

Ikkala tarafdan 5x ni ayirish.

$$6x^{2}-8x-5x=0$$

-13x ni olish uchun -8x va -5x ni birlashtirish.

$$6x^{2}-13x=0$$

x omili.

$$x\left(6x-13\right)=0$$

Tenglamani yechish uchun x=0 va 6x-13=0 ni yeching.

$$x=0 x=\frac{13}{6}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga 3x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-8x=5x$$

Ikkala tarafdan 5x ni ayirish.

$$6x^{2}-8x-5x=0$$

-13x ni olish uchun -8x va -5x ni birlashtirish.

$$6x^{2}-13x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -13 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}}}{2\times 6}$$

\left(-13\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-13\right)±13}{2\times 6}$$

-13 ning teskarisi 13 ga teng.

$$x=\frac{13±13}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{13±13}{12}$$

x=\frac{13±13}{12} tenglamasini yeching, bunda ± musbat. 13 ni 13 ga qo'shish.

$$x=\frac{26}{12}$$

\frac{26}{12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{13}{6}$$

x=\frac{13±13}{12} tenglamasini yeching, bunda ± manfiy. 13 dan 13 ni ayirish.

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

0 ni 12 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{13}{6} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

2x ga 3x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-8x=5x$$

Ikkala tarafdan 5x ni ayirish.

$$6x^{2}-8x-5x=0$$

-13x ni olish uchun -8x va -5x ni birlashtirish.

$$6x^{2}-13x=0$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-13x}{6}=\frac{0}{6}$$

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

$$x^{2}-\frac{13}{6}x=\frac{0}{6}$$

0 ni 6 ga bo'lish.

$$x^{2}-\frac{13}{6}x=0$$

-\frac{13}{6} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{13}{12} olish uchun. Keyin, -\frac{13}{12} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{13}{6}x+\left(-\frac{13}{12}\right)^{2}=\left(-\frac{13}{12}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{13}{12} kvadratini chiqarish.

$$x^{2}-\frac{13}{6}x+\frac{169}{144}=\frac{169}{144}$$

x^{2}-\frac{13}{6}x+\frac{169}{144} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{13}{12}\right)^{2}=\frac{169}{144}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{13}{12}\right)^{2}}=\sqrt{\frac{169}{144}}$$

Qisqartirish.

$$x-\frac{13}{12}=\frac{13}{12} x-\frac{13}{12}=-\frac{13}{12}$$

\frac{13}{12} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{13}{6} x=0$$