9x^2-95x-44 eching

$$9 x ^ { 2 } - 95 x - 44$$

Omil

$$\left(x-11\right)\left(9x+4\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 9x^{2}+ax+bx-44 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-95 ab=9\left(-44\right)=-396$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -396-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-396 2,-198 3,-132 4,-99 6,-66 9,-44 11,-36 12,-33 18,-22$$

Har bir juftlik yigʻindisini hisoblang.

$$1-396=-395 2-198=-196 3-132=-129 4-99=-95 6-66=-60 9-44=-35 11-36=-25 12-33=-21 18-22=-4$$

Yechim – -95 yigʻindisini beruvchi juftlik.

$$a=-99 b=4$$

9x^{2}-95x-44 ni \left(9x^{2}-99x\right)+\left(4x-44\right) sifatida qaytadan yozish.

$$\left(9x^{2}-99x\right)+\left(4x-44\right)$$

Birinchi guruhda 9x ni va ikkinchi guruhda 4 ni faktordan chiqaring.

$$9x\left(x-11\right)+4\left(x-11\right)$$

Distributiv funktsiyasidan foydalangan holda x-11 umumiy terminini chiqaring.

$$\left(x-11\right)\left(9x+4\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$9x^{2}-95x-44=0$$

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.

$$x=\frac{-\left(-95\right)±\sqrt{\left(-95\right)^{2}-4\times 9\left(-44\right)}}{2\times 9}$$

-95 kvadratini chiqarish.

$$x=\frac{-\left(-95\right)±\sqrt{9025-4\times 9\left(-44\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$x=\frac{-\left(-95\right)±\sqrt{9025-36\left(-44\right)}}{2\times 9}$$

-36 ni -44 marotabaga ko'paytirish.

$$x=\frac{-\left(-95\right)±\sqrt{9025+1584}}{2\times 9}$$

9025 ni 1584 ga qo'shish.

$$x=\frac{-\left(-95\right)±\sqrt{10609}}{2\times 9}$$

10609 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-95\right)±103}{2\times 9}$$

-95 ning teskarisi 95 ga teng.

$$x=\frac{95±103}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$x=\frac{95±103}{18}$$

x=\frac{95±103}{18} tenglamasini yeching, bunda ± musbat. 95 ni 103 ga qo'shish.

$$x=\frac{198}{18}$$

198 ni 18 ga bo'lish.

$$x=11$$

x=\frac{95±103}{18} tenglamasini yeching, bunda ± manfiy. 95 dan 103 ni ayirish.

$$x=-\frac{8}{18}$$

\frac{-8}{18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{4}{9}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 11 ga va x_{2} uchun -\frac{4}{9} ga bo‘ling.

$$9x^{2}-95x-44=9\left(x-11\right)\left(x-\left(-\frac{4}{9}\right)\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$9x^{2}-95x-44=9\left(x-11\right)\left(x+\frac{4}{9}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{4}{9} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$9x^{2}-95x-44=9\left(x-11\right)\times \frac{9x+4}{9}$$

9 va 9 ichida eng katta umumiy 9 faktorini bekor qiling.

$$9x^{2}-95x-44=\left(x-11\right)\left(9x+4\right)$$

Baholash

$$\left(x-11\right)\left(9x+4\right)$$