2x^2+12x-14 eching

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

Omil

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

Yechim qadamlari

2 omili.

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

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

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

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.

$$a=-1 b=7$$

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

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

Birinchi guruhda x ni va ikkinchi guruhda 7 ni faktordan chiqaring.

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

Distributiv funktsiyasidan foydalangan holda x-1 umumiy terminini chiqaring.

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

Toʻliq ajratilgan ifodani qaytadan yozing.

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

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.

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

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.

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

12 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-8\left(-14\right)}}{2\times 2}$$

-8 ni -14 marotabaga ko'paytirish.

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

144 ni 112 ga qo'shish.

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

256 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±16}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-12±16}{4}$$

x=\frac{-12±16}{4} tenglamasini yeching, bunda ± musbat. -12 ni 16 ga qo'shish.

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

4 ni 4 ga bo'lish.

$$x=1$$

x=\frac{-12±16}{4} tenglamasini yeching, bunda ± manfiy. -12 dan 16 ni ayirish.

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

-28 ni 4 ga bo'lish.

$$x=-7$$

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

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

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

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

Baholash

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