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

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

x uchun yechish

$$x = \frac{\sqrt{265} + 17}{6} \approx 5,546470099$$

$$x=\frac{17-\sqrt{265}}{6}\approx 0,120196567$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

$$3x^{2}-12x=4x+x-2$$

5x ni olish uchun 4x va x ni birlashtirish.

$$3x^{2}-12x=5x-2$$

Ikkala tarafdan 5x ni ayirish.

$$3x^{2}-12x-5x=-2$$

-17x ni olish uchun -12x va -5x ni birlashtirish.

$$3x^{2}-17x=-2$$

2 ni ikki tarafga qo’shing.

$$3x^{2}-17x+2=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 3 ni a, -17 ni b va 2 ni c bilan almashtiring.

$$x=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 3\times 2}}{2\times 3}$$

-17 kvadratini chiqarish.

$$x=\frac{-\left(-17\right)±\sqrt{289-4\times 3\times 2}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-17\right)±\sqrt{289-12\times 2}}{2\times 3}$$

-12 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-17\right)±\sqrt{289-24}}{2\times 3}$$

289 ni -24 ga qo'shish.

$$x=\frac{-\left(-17\right)±\sqrt{265}}{2\times 3}$$

-17 ning teskarisi 17 ga teng.

$$x=\frac{17±\sqrt{265}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{17±\sqrt{265}}{6}$$

x=\frac{17±\sqrt{265}}{6} tenglamasini yeching, bunda ± musbat. 17 ni \sqrt{265} ga qo'shish.

$$x=\frac{\sqrt{265}+17}{6}$$

x=\frac{17±\sqrt{265}}{6} tenglamasini yeching, bunda ± manfiy. 17 dan \sqrt{265} ni ayirish.

$$x=\frac{17-\sqrt{265}}{6}$$

Tenglama yechildi.

$$x=\frac{\sqrt{265}+17}{6} x=\frac{17-\sqrt{265}}{6}$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$3x^{2}-12x=4x+x-2$$

5x ni olish uchun 4x va x ni birlashtirish.

$$3x^{2}-12x=5x-2$$

Ikkala tarafdan 5x ni ayirish.

$$3x^{2}-12x-5x=-2$$

-17x ni olish uchun -12x va -5x ni birlashtirish.

$$3x^{2}-17x=-2$$

Ikki tarafini 3 ga bo‘ling.

$$\frac{3x^{2}-17x}{3}=-\frac{2}{3}$$

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

$$x^{2}-\frac{17}{3}x=-\frac{2}{3}$$

-\frac{17}{3} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{17}{6} olish uchun. Keyin, -\frac{17}{6} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{17}{3}x+\left(-\frac{17}{6}\right)^{2}=-\frac{2}{3}+\left(-\frac{17}{6}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{17}{6} kvadratini chiqarish.

$$x^{2}-\frac{17}{3}x+\frac{289}{36}=-\frac{2}{3}+\frac{289}{36}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{2}{3} ni \frac{289}{36} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-\frac{17}{3}x+\frac{289}{36}=\frac{265}{36}$$

x^{2}-\frac{17}{3}x+\frac{289}{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.

$$\left(x-\frac{17}{6}\right)^{2}=\frac{265}{36}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{17}{6}\right)^{2}}=\sqrt{\frac{265}{36}}$$

Qisqartirish.

$$x-\frac{17}{6}=\frac{\sqrt{265}}{6} x-\frac{17}{6}=-\frac{\sqrt{265}}{6}$$

\frac{17}{6} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{265}+17}{6} x=\frac{17-\sqrt{265}}{6}$$