2s^2-13s-7 eching

$$2 s ^ { 2 } - 13 s - 7$$

Omil

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

Yechim qadamlari

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

$$a+b=-13 ab=2\left(-7\right)=-14$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga 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.

$$a=-14 b=1$$

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

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

2s^{2}-14s ichida 2s ni ajrating.

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

Distributiv funktsiyasidan foydalangan holda s-7 umumiy terminini chiqaring.

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

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.

$$2s^{2}-13s-7=0$$

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.

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

-13 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

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

-8 ni -7 marotabaga ko'paytirish.

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

169 ni 56 ga qo'shish.

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

225 ning kvadrat ildizini chiqarish.

$$s=\frac{-\left(-13\right)±15}{2\times 2}$$

-13 ning teskarisi 13 ga teng.

$$s=\frac{13±15}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$s=\frac{13±15}{4}$$

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

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

28 ni 4 ga bo'lish.

$$s=7$$

s=\frac{13±15}{4} tenglamasini yeching, bunda ± manfiy. 13 dan 15 ni ayirish.

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

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

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

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

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

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

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

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

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

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

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

Baholash

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