-2x^2+13x+7 eching

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

Omil

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

Yechim qadamlari

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

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

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.

$$a=14 b=-1$$

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

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

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

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

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

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

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.

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

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.

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

13 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-13±\sqrt{169+8\times 7}}{2\left(-2\right)}$$

8 ni 7 marotabaga ko'paytirish.

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

169 ni 56 ga qo'shish.

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

225 ning kvadrat ildizini chiqarish.

$$x=\frac{-13±15}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-13±15}{-4}$$

x=\frac{-13±15}{-4} tenglamasini yeching, bunda ± musbat. -13 ni 15 ga qo'shish.

$$x=\frac{2}{-4}$$

\frac{2}{-4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{2}$$

x=\frac{-13±15}{-4} tenglamasini yeching, bunda ± manfiy. -13 dan 15 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 -\frac{1}{2} ga va x_{2} uchun 7 ga bo‘ling.

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

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

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

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

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

-2 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

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

Baholash

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