(x-4)(4x-3)=12 eching

$$( x - 4 ) ( 4 x - 3 ) = 12$$

x uchun yechish

$$x = \frac{19}{4} = 4\frac{3}{4} = 4,75$$

$$x=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-4 ga 4x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4x^{2}-19x+12=12$$

Ikkala tarafdan 12 ni ayirish.

$$4x^{2}-19x+12-12=0$$

0 olish uchun 12 dan 12 ni ayirish.

$$4x^{2}-19x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 4 ni a, -19 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-19\right)±\sqrt{\left(-19\right)^{2}}}{2\times 4}$$

\left(-19\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-19\right)±19}{2\times 4}$$

-19 ning teskarisi 19 ga teng.

$$x=\frac{19±19}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{19±19}{8}$$

x=\frac{19±19}{8} tenglamasini yeching, bunda ± musbat. 19 ni 19 ga qo'shish.

$$x=\frac{38}{8}$$

\frac{38}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{19}{4}$$

x=\frac{19±19}{8} tenglamasini yeching, bunda ± manfiy. 19 dan 19 ni ayirish.

$$x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{19}{4} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

x-4 ga 4x-3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$4x^{2}-19x+12=12$$

Ikkala tarafdan 12 ni ayirish.

$$4x^{2}-19x=12-12$$

0 olish uchun 12 dan 12 ni ayirish.

$$4x^{2}-19x=0$$

Ikki tarafini 4 ga bo‘ling.

$$\frac{4x^{2}-19x}{4}=\frac{0}{4}$$

4 ga bo'lish 4 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{19}{4}x=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$x^{2}-\frac{19}{4}x=0$$

-\frac{19}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{19}{8} olish uchun. Keyin, -\frac{19}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{19}{4}x+\left(-\frac{19}{8}\right)^{2}=\left(-\frac{19}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{19}{8} kvadratini chiqarish.

$$x^{2}-\frac{19}{4}x+\frac{361}{64}=\frac{361}{64}$$

x^{2}-\frac{19}{4}x+\frac{361}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{19}{8}\right)^{2}=\frac{361}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{19}{8}\right)^{2}}=\sqrt{\frac{361}{64}}$$

Qisqartirish.

$$x-\frac{19}{8}=\frac{19}{8} x-\frac{19}{8}=-\frac{19}{8}$$

\frac{19}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{19}{4} x=0$$