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

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

x uchun yechish

$$x=-1$$

$$x=4$$

Kvadrat tenglamalaridan foydalanish qoidalari

2x-4 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-12x+16=\left(5-x\right)\left(4-x\right)$$

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

$$2x^{2}-12x+16=20-9x+x^{2}$$

Ikkala tarafdan 20 ni ayirish.

$$2x^{2}-12x+16-20=-9x+x^{2}$$

-4 olish uchun 16 dan 20 ni ayirish.

$$2x^{2}-12x-4=-9x+x^{2}$$

9x ni ikki tarafga qo’shing.

$$2x^{2}-12x-4+9x=x^{2}$$

-3x ni olish uchun -12x va 9x ni birlashtirish.

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

Ikkala tarafdan x^{2} ni ayirish.

$$2x^{2}-3x-4-x^{2}=0$$

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

$$x^{2}-3x-4=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va -4 ni c bilan almashtiring.

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

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-4\right)}}{2}$$

-4 ni -4 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+16}}{2}$$

9 ni 16 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{25}}{2}$$

25 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±5}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±5}{2}$$

x=\frac{3±5}{2} tenglamasini yeching, bunda ± musbat. 3 ni 5 ga qo'shish.

$$x=\frac{8}{2}$$

8 ni 2 ga bo'lish.

$$x=4$$

x=\frac{3±5}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 5 ni ayirish.

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

-2 ni 2 ga bo'lish.

$$x=-1$$

Tenglama yechildi.

$$x=4 x=-1$$

Kvadratni yakunlash bo'yicha qadamlar

2x-4 ga x-4 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}-12x+16=\left(5-x\right)\left(4-x\right)$$

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

$$2x^{2}-12x+16=20-9x+x^{2}$$

9x ni ikki tarafga qo’shing.

$$2x^{2}-12x+16+9x=20+x^{2}$$

-3x ni olish uchun -12x va 9x ni birlashtirish.

$$2x^{2}-3x+16=20+x^{2}$$

Ikkala tarafdan x^{2} ni ayirish.

$$2x^{2}-3x+16-x^{2}=20$$

x^{2} ni olish uchun 2x^{2} va -x^{2} ni birlashtirish.

$$x^{2}-3x+16=20$$

Ikkala tarafdan 16 ni ayirish.

$$x^{2}-3x=20-16$$

4 olish uchun 20 dan 16 ni ayirish.

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

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

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

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=4+\frac{9}{4}$$

4 ni \frac{9}{4} ga qo'shish.

$$x^{2}-3x+\frac{9}{4}=\frac{25}{4}$$

x^{2}-3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

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

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=4 x=-1$$