14x^2+12x-2 eching

$$14 x ^ { 2 } + 12 x - 2$$

Omil

$$2\left(7x-1\right)\left(x+1\right)$$

Yechim qadamlari

2 omili.

$$2\left(7x^{2}+6x-1\right)$$

Hisoblang: 7x^{2}+6x-1. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 7x^{2}+ax+bx-1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=6 ab=7\left(-1\right)=-7$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$a=-1 b=7$$

7x^{2}+6x-1 ni \left(7x^{2}-x\right)+\left(7x-1\right) sifatida qaytadan yozish.

$$\left(7x^{2}-x\right)+\left(7x-1\right)$$

7x^{2}-x ichida x ni ajrating.

$$x\left(7x-1\right)+7x-1$$

Distributiv funktsiyasidan foydalangan holda 7x-1 umumiy terminini chiqaring.

$$\left(7x-1\right)\left(x+1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$2\left(7x-1\right)\left(x+1\right)$$

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.

$$14x^{2}+12x-2=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 14\left(-2\right)}}{2\times 14}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 14\left(-2\right)}}{2\times 14}$$

-4 ni 14 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-56\left(-2\right)}}{2\times 14}$$

-56 ni -2 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144+112}}{2\times 14}$$

144 ni 112 ga qo'shish.

$$x=\frac{-12±\sqrt{256}}{2\times 14}$$

256 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±16}{2\times 14}$$

2 ni 14 marotabaga ko'paytirish.

$$x=\frac{-12±16}{28}$$

x=\frac{-12±16}{28} tenglamasini yeching, bunda ± musbat. -12 ni 16 ga qo'shish.

$$x=\frac{4}{28}$$

\frac{4}{28} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{7}$$

x=\frac{-12±16}{28} tenglamasini yeching, bunda ± manfiy. -12 dan 16 ni ayirish.

$$x=-\frac{28}{28}$$

-28 ni 28 ga bo'lish.

$$x=-1$$

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

$$14x^{2}+12x-2=14\left(x-\frac{1}{7}\right)\left(x-\left(-1\right)\right)$$

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

$$14x^{2}+12x-2=14\left(x-\frac{1}{7}\right)\left(x+1\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{7} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$14x^{2}+12x-2=14\times \frac{7x-1}{7}\left(x+1\right)$$

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

$$14x^{2}+12x-2=2\left(7x-1\right)\left(x+1\right)$$

Baholash

$$2\left(7x-1\right)\left(x+1\right)$$