-x^2-3x+28= eching

$$- x ^ { 2 } - 3 x + 28 =$$

Omil

$$\left(4-x\right)\left(x+7\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx+28 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-3 ab=-28=-28$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -28-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-28 2,-14 4,-7$$

Har bir juftlik yigʻindisini hisoblang.

$$1-28=-27 2-14=-12 4-7=-3$$

Yechim – -3 yigʻindisini beruvchi juftlik.

$$a=4 b=-7$$

-x^{2}-3x+28 ni \left(-x^{2}+4x\right)+\left(-7x+28\right) sifatida qaytadan yozish.

$$\left(-x^{2}+4x\right)+\left(-7x+28\right)$$

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

$$x\left(-x+4\right)+7\left(-x+4\right)$$

Distributiv funktsiyasidan foydalangan holda -x+4 umumiy terminini chiqaring.

$$\left(-x+4\right)\left(x+7\right)$$

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.

$$-x^{2}-3x+28=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-1\right)\times 28}}{2\left(-1\right)}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-1\right)\times 28}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+4\times 28}}{2\left(-1\right)}$$

4 ni 28 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+112}}{2\left(-1\right)}$$

9 ni 112 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{121}}{2\left(-1\right)}$$

121 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±11}{2\left(-1\right)}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±11}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{3±11}{-2}$$

x=\frac{3±11}{-2} tenglamasini yeching, bunda ± musbat. 3 ni 11 ga qo'shish.

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

14 ni -2 ga bo'lish.

$$x=-7$$

x=\frac{3±11}{-2} tenglamasini yeching, bunda ± manfiy. 3 dan 11 ni ayirish.

$$x=-\frac{8}{-2}$$

-8 ni -2 ga bo'lish.

$$x=4$$

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 4 ga bo‘ling.

$$-x^{2}-3x+28=-\left(x-\left(-7\right)\right)\left(x-4\right)$$

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

$$-x^{2}-3x+28=-\left(x+7\right)\left(x-4\right)$$

Baholash

$$\left(4-x\right)\left(x+7\right)$$