2x(3x-6)=3(3x-6) eching

$$2 x ( 3 x - 6 ) = 3 ( 3 x - 6 )$$

x uchun yechish

$$x=2$$

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

Kvadrat tenglamalaridan foydalanish qoidalari

2x ga 3x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-12x=3\left(3x-6\right)$$

3 ga 3x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-12x=9x-18$$

Ikkala tarafdan 9x ni ayirish.

$$6x^{2}-12x-9x=-18$$

-21x ni olish uchun -12x va -9x ni birlashtirish.

$$6x^{2}-21x=-18$$

18 ni ikki tarafga qo’shing.

$$6x^{2}-21x+18=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 6 ni a, -21 ni b va 18 ni c bilan almashtiring.

$$x=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 6\times 18}}{2\times 6}$$

-21 kvadratini chiqarish.

$$x=\frac{-\left(-21\right)±\sqrt{441-4\times 6\times 18}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-21\right)±\sqrt{441-24\times 18}}{2\times 6}$$

-24 ni 18 marotabaga ko'paytirish.

$$x=\frac{-\left(-21\right)±\sqrt{441-432}}{2\times 6}$$

441 ni -432 ga qo'shish.

$$x=\frac{-\left(-21\right)±\sqrt{9}}{2\times 6}$$

9 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-21\right)±3}{2\times 6}$$

-21 ning teskarisi 21 ga teng.

$$x=\frac{21±3}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{21±3}{12}$$

x=\frac{21±3}{12} tenglamasini yeching, bunda ± musbat. 21 ni 3 ga qo'shish.

$$x=\frac{24}{12}$$

24 ni 12 ga bo'lish.

$$x=2$$

x=\frac{21±3}{12} tenglamasini yeching, bunda ± manfiy. 21 dan 3 ni ayirish.

$$x=\frac{18}{12}$$

\frac{18}{12} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{2}$$

Tenglama yechildi.

$$x=2 x=\frac{3}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

2x ga 3x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-12x=3\left(3x-6\right)$$

3 ga 3x-6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6x^{2}-12x=9x-18$$

Ikkala tarafdan 9x ni ayirish.

$$6x^{2}-12x-9x=-18$$

-21x ni olish uchun -12x va -9x ni birlashtirish.

$$6x^{2}-21x=-18$$

Ikki tarafini 6 ga bo‘ling.

$$\frac{6x^{2}-21x}{6}=-\frac{18}{6}$$

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

$$x^{2}+\left(-\frac{21}{6}\right)x=-\frac{18}{6}$$

\frac{-21}{6} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{7}{2}x=-\frac{18}{6}$$

-18 ni 6 ga bo'lish.

$$x^{2}-\frac{7}{2}x=-3$$

-\frac{7}{2} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{7}{4} olish uchun. Keyin, -\frac{7}{4} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{7}{2}x+\left(-\frac{7}{4}\right)^{2}=-3+\left(-\frac{7}{4}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{7}{4} kvadratini chiqarish.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=-3+\frac{49}{16}$$

-3 ni \frac{49}{16} ga qo'shish.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=\frac{1}{16}$$

x^{2}-\frac{7}{2}x+\frac{49}{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.

$$\left(x-\frac{7}{4}\right)^{2}=\frac{1}{16}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{7}{4}\right)^{2}}=\sqrt{\frac{1}{16}}$$

Qisqartirish.

$$x-\frac{7}{4}=\frac{1}{4} x-\frac{7}{4}=-\frac{1}{4}$$

\frac{7}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x=2 x=\frac{3}{2}$$