-7x^2+13x+2 eching

$$- 7 x ^ { 2 } + 13 x + 2$$

Omil

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

Yechim qadamlari

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

$$a+b=13 ab=-7\times 2=-14$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -14-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,14 -2,7$$

Har bir juftlik yigʻindisini hisoblang.

$$-1+14=13 -2+7=5$$

Yechim – 13 yigʻindisini beruvchi juftlik.

$$a=14 b=-1$$

-7x^{2}+13x+2 ni \left(-7x^{2}+14x\right)+\left(-x+2\right) sifatida qaytadan yozish.

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

-7x^{2}+14x ichida 7x ni ajrating.

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

Distributiv funktsiyasidan foydalangan holda -x+2 umumiy terminini chiqaring.

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

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.

$$-7x^{2}+13x+2=0$$

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.

$$x=\frac{-13±\sqrt{13^{2}-4\left(-7\right)\times 2}}{2\left(-7\right)}$$

13 kvadratini chiqarish.

$$x=\frac{-13±\sqrt{169-4\left(-7\right)\times 2}}{2\left(-7\right)}$$

-4 ni -7 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{169+28\times 2}}{2\left(-7\right)}$$

28 ni 2 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{169+56}}{2\left(-7\right)}$$

169 ni 56 ga qo'shish.

$$x=\frac{-13±\sqrt{225}}{2\left(-7\right)}$$

225 ning kvadrat ildizini chiqarish.

$$x=\frac{-13±15}{2\left(-7\right)}$$

2 ni -7 marotabaga ko'paytirish.

$$x=\frac{-13±15}{-14}$$

x=\frac{-13±15}{-14} tenglamasini yeching, bunda ± musbat. -13 ni 15 ga qo'shish.

$$x=\frac{2}{-14}$$

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

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

x=\frac{-13±15}{-14} tenglamasini yeching, bunda ± manfiy. -13 dan 15 ni ayirish.

$$x=-\frac{28}{-14}$$

-28 ni -14 ga bo'lish.

$$x=2$$

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 2 ga bo‘ling.

$$-7x^{2}+13x+2=-7\left(x-\left(-\frac{1}{7}\right)\right)\left(x-2\right)$$

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

$$-7x^{2}+13x+2=-7\left(x+\frac{1}{7}\right)\left(x-2\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{7} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$-7x^{2}+13x+2=-7\times \frac{-7x-1}{-7}\left(x-2\right)$$

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

$$-7x^{2}+13x+2=\left(-7x-1\right)\left(x-2\right)$$

Baholash

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