-x^2-2x+35 eching

$$- x ^ { 2 } - 2 x + 35$$

Omil

$$\left(5-x\right)\left(x+7\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx+35 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=-35=-35$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -35-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-35 5,-7$$

Har bir juftlik yigʻindisini hisoblang.

$$1-35=-34 5-7=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$a=5 b=-7$$

-x^{2}-2x+35 ni \left(-x^{2}+5x\right)+\left(-7x+35\right) sifatida qaytadan yozish.

$$\left(-x^{2}+5x\right)+\left(-7x+35\right)$$

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

$$x\left(-x+5\right)+7\left(-x+5\right)$$

Distributiv funktsiyasidan foydalangan holda -x+5 umumiy terminini chiqaring.

$$\left(-x+5\right)\left(x+7\right)$$

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.

$$-x^{2}-2x+35=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 35}}{2\left(-1\right)}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\times 35}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\times 35}}{2\left(-1\right)}$$

4 ni 35 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+140}}{2\left(-1\right)}$$

4 ni 140 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{144}}{2\left(-1\right)}$$

144 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±12}{2\left(-1\right)}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±12}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±12}{-2}$$

x=\frac{2±12}{-2} tenglamasini yeching, bunda ± musbat. 2 ni 12 ga qo'shish.

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

14 ni -2 ga bo'lish.

$$x=-7$$

x=\frac{2±12}{-2} tenglamasini yeching, bunda ± manfiy. 2 dan 12 ni ayirish.

$$x=-\frac{10}{-2}$$

-10 ni -2 ga bo'lish.

$$x=5$$

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 5 ga bo‘ling.

$$-x^{2}-2x+35=-\left(x-\left(-7\right)\right)\left(x-5\right)$$

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

$$-x^{2}-2x+35=-\left(x+7\right)\left(x-5\right)$$

Baholash

$$\left(5-x\right)\left(x+7\right)$$