x^2-9x-19/4=0 eching

$${ x }^{ 2 } -9x- \frac{ 19 }{ 4 } = 0$$

x uchun yechish

$$x=-\frac{1}{2}=-0,5$$

$$x = \frac{19}{2} = 9\frac{1}{2} = 9,5$$

Kvadrat tenglamalaridan foydalanish qoidalari

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-9x-\frac{19}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -9 ni b va -\frac{19}{4} ni c bilan almashtiring.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\left(-\frac{19}{4}\right)}}{2}$$

-9 kvadratini chiqarish.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\left(-\frac{19}{4}\right)}}{2}$$

-4 ni -\frac{19}{4} marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81+19}}{2}$$

81 ni 19 ga qo'shish.

$$x=\frac{-\left(-9\right)±\sqrt{100}}{2}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±10}{2}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±10}{2}$$

x=\frac{9±10}{2} tenglamasini yeching, bunda ± musbat. 9 ni 10 ga qo'shish.

$$x=\frac{19}{2}$$

x=\frac{9±10}{2} tenglamasini yeching, bunda ± manfiy. 9 dan 10 ni ayirish.

$$x=-\frac{1}{2}$$

Tenglama yechildi.

$$x=\frac{19}{2} x=-\frac{1}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-9x-\frac{19}{4}=0$$

\frac{19}{4} ni tenglamaning ikkala tarafiga qo'shish.

$$x^{2}-9x-\frac{19}{4}-\left(-\frac{19}{4}\right)=-\left(-\frac{19}{4}\right)$$

O‘zidan -\frac{19}{4} ayirilsa 0 qoladi.

$$x^{2}-9x=-\left(-\frac{19}{4}\right)$$

0 dan -\frac{19}{4} ni ayirish.

$$x^{2}-9x=\frac{19}{4}$$

-9 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{2} olish uchun. Keyin, -\frac{9}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=\frac{19}{4}+\left(-\frac{9}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{2} kvadratini chiqarish.

$$x^{2}-9x+\frac{81}{4}=\frac{19+81}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{19}{4} ni \frac{81}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-9x+\frac{81}{4}=25$$

x^{2}-9x+\frac{81}{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.

$$\left(x-\frac{9}{2}\right)^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{25}$$

Qisqartirish.

$$x-\frac{9}{2}=5 x-\frac{9}{2}=-5$$

\frac{9}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{19}{2} x=-\frac{1}{2}$$