7c^2-4c-20 eching

$$7 c ^ { 2 } - 4 c - 20$$

Omil

$$\left(c-2\right)\left(7c+10\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 7c^{2}+ac+bc-20 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-4 ab=7\left(-20\right)=-140$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -140-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-140 2,-70 4,-35 5,-28 7,-20 10,-14$$

Har bir juftlik yigʻindisini hisoblang.

$$1-140=-139 2-70=-68 4-35=-31 5-28=-23 7-20=-13 10-14=-4$$

Yechim – -4 yigʻindisini beruvchi juftlik.

$$a=-14 b=10$$

7c^{2}-4c-20 ni \left(7c^{2}-14c\right)+\left(10c-20\right) sifatida qaytadan yozish.

$$\left(7c^{2}-14c\right)+\left(10c-20\right)$$

Birinchi guruhda 7c ni va ikkinchi guruhda 10 ni faktordan chiqaring.

$$7c\left(c-2\right)+10\left(c-2\right)$$

Distributiv funktsiyasidan foydalangan holda c-2 umumiy terminini chiqaring.

$$\left(c-2\right)\left(7c+10\right)$$

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.

$$7c^{2}-4c-20=0$$

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.

$$c=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 7\left(-20\right)}}{2\times 7}$$

-4 kvadratini chiqarish.

$$c=\frac{-\left(-4\right)±\sqrt{16-4\times 7\left(-20\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$c=\frac{-\left(-4\right)±\sqrt{16-28\left(-20\right)}}{2\times 7}$$

-28 ni -20 marotabaga ko'paytirish.

$$c=\frac{-\left(-4\right)±\sqrt{16+560}}{2\times 7}$$

16 ni 560 ga qo'shish.

$$c=\frac{-\left(-4\right)±\sqrt{576}}{2\times 7}$$

576 ning kvadrat ildizini chiqarish.

$$c=\frac{-\left(-4\right)±24}{2\times 7}$$

-4 ning teskarisi 4 ga teng.

$$c=\frac{4±24}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$c=\frac{4±24}{14}$$

c=\frac{4±24}{14} tenglamasini yeching, bunda ± musbat. 4 ni 24 ga qo'shish.

$$c=\frac{28}{14}$$

28 ni 14 ga bo'lish.

$$c=2$$

c=\frac{4±24}{14} tenglamasini yeching, bunda ± manfiy. 4 dan 24 ni ayirish.

$$c=-\frac{20}{14}$$

\frac{-20}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$c=-\frac{10}{7}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 2 ga va x_{2} uchun -\frac{10}{7} ga bo‘ling.

$$7c^{2}-4c-20=7\left(c-2\right)\left(c-\left(-\frac{10}{7}\right)\right)$$

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

$$7c^{2}-4c-20=7\left(c-2\right)\left(c+\frac{10}{7}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{10}{7} ni c ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$7c^{2}-4c-20=7\left(c-2\right)\times \frac{7c+10}{7}$$

7 va 7 ichida eng katta umumiy 7 faktorini bekor qiling.

$$7c^{2}-4c-20=\left(c-2\right)\left(7c+10\right)$$

Baholash

$$\left(c-2\right)\left(7c+10\right)$$