7x^2-2x-9 eching

$$7 { x }^{ 2 } -2x-9$$

Omil

$$\left(7x-9\right)\left(x+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 7x^{2}+ax+bx-9 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=7\left(-9\right)=-63$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -63-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-63 3,-21 7,-9$$

Har bir juftlik yigʻindisini hisoblang.

$$1-63=-62 3-21=-18 7-9=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$a=-9 b=7$$

7x^{2}-2x-9 ni \left(7x^{2}-9x\right)+\left(7x-9\right) sifatida qaytadan yozish.

$$\left(7x^{2}-9x\right)+\left(7x-9\right)$$

7x^{2}-9x ichida x ni ajrating.

$$x\left(7x-9\right)+7x-9$$

Distributiv funktsiyasidan foydalangan holda 7x-9 umumiy terminini chiqaring.

$$\left(7x-9\right)\left(x+1\right)$$

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.

$$7x^{2}-2x-9=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 7\left(-9\right)}}{2\times 7}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 7\left(-9\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4-28\left(-9\right)}}{2\times 7}$$

-28 ni -9 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+252}}{2\times 7}$$

4 ni 252 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{256}}{2\times 7}$$

256 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±16}{2\times 7}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±16}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{2±16}{14}$$

x=\frac{2±16}{14} tenglamasini yeching, bunda ± musbat. 2 ni 16 ga qo'shish.

$$x=\frac{18}{14}$$

\frac{18}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{9}{7}$$

x=\frac{2±16}{14} tenglamasini yeching, bunda ± manfiy. 2 dan 16 ni ayirish.

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

-14 ni 14 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{9}{7} ga va x_{2} uchun -1 ga bo‘ling.

$$7x^{2}-2x-9=7\left(x-\frac{9}{7}\right)\left(x-\left(-1\right)\right)$$

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

$$7x^{2}-2x-9=7\left(x-\frac{9}{7}\right)\left(x+1\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{9}{7} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$7x^{2}-2x-9=7\times \frac{7x-9}{7}\left(x+1\right)$$

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

$$7x^{2}-2x-9=\left(7x-9\right)\left(x+1\right)$$

Baholash

$$\left(7x-9\right)\left(x+1\right)$$