(x-16)(x-19)=25/64 eching

$$( x - 16 ) ( x - 19 ) = \frac { 25 } { 64 }$$

x uchun yechish

$$x = \frac{153}{8} = 19\frac{1}{8} = 19,125$$

$$x = \frac{127}{8} = 15\frac{7}{8} = 15,875$$

Kvadrat tenglamalaridan foydalanish qoidalari

x-16 ga x-19 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-35x+304=\frac{25}{64}$$

Ikkala tarafdan \frac{25}{64} ni ayirish.

$$x^{2}-35x+304-\frac{25}{64}=0$$

\frac{19431}{64} olish uchun 304 dan \frac{25}{64} ni ayirish.

$$x^{2}-35x+\frac{19431}{64}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -35 ni b va \frac{19431}{64} ni c bilan almashtiring.

$$x=\frac{-\left(-35\right)±\sqrt{\left(-35\right)^{2}-4\times \frac{19431}{64}}}{2}$$

-35 kvadratini chiqarish.

$$x=\frac{-\left(-35\right)±\sqrt{1225-4\times \frac{19431}{64}}}{2}$$

-4 ni \frac{19431}{64} marotabaga ko'paytirish.

$$x=\frac{-\left(-35\right)±\sqrt{1225-\frac{19431}{16}}}{2}$$

1225 ni -\frac{19431}{16} ga qo'shish.

$$x=\frac{-\left(-35\right)±\sqrt{\frac{169}{16}}}{2}$$

\frac{169}{16} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-35\right)±\frac{13}{4}}{2}$$

-35 ning teskarisi 35 ga teng.

$$x=\frac{35±\frac{13}{4}}{2}$$

x=\frac{35±\frac{13}{4}}{2} tenglamasini yeching, bunda ± musbat. 35 ni \frac{13}{4} ga qo'shish.

$$x=\frac{\frac{153}{4}}{2}$$

\frac{153}{4} ni 2 ga bo'lish.

$$x=\frac{153}{8}$$

x=\frac{35±\frac{13}{4}}{2} tenglamasini yeching, bunda ± manfiy. 35 dan \frac{13}{4} ni ayirish.

$$x=\frac{\frac{127}{4}}{2}$$

\frac{127}{4} ni 2 ga bo'lish.

$$x=\frac{127}{8}$$

Tenglama yechildi.

$$x=\frac{153}{8} x=\frac{127}{8}$$

Kvadratni yakunlash bo'yicha qadamlar

x-16 ga x-19 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}-35x+304=\frac{25}{64}$$

Ikkala tarafdan 304 ni ayirish.

$$x^{2}-35x=\frac{25}{64}-304$$

-\frac{19431}{64} olish uchun \frac{25}{64} dan 304 ni ayirish.

$$x^{2}-35x=-\frac{19431}{64}$$

-35 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{35}{2} olish uchun. Keyin, -\frac{35}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-35x+\left(-\frac{35}{2}\right)^{2}=-\frac{19431}{64}+\left(-\frac{35}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{35}{2} kvadratini chiqarish.

$$x^{2}-35x+\frac{1225}{4}=-\frac{19431}{64}+\frac{1225}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali -\frac{19431}{64} ni \frac{1225}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-35x+\frac{1225}{4}=\frac{169}{64}$$

x^{2}-35x+\frac{1225}{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.

$$\left(x-\frac{35}{2}\right)^{2}=\frac{169}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{35}{2}\right)^{2}}=\sqrt{\frac{169}{64}}$$

Qisqartirish.

$$x-\frac{35}{2}=\frac{13}{8} x-\frac{35}{2}=-\frac{13}{8}$$

\frac{35}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{153}{8} x=\frac{127}{8}$$