7w^2+42w-189 eching

$$7 w ^ { 2 } + 42 w - 189$$

Omil

$$7\left(w-3\right)\left(w+9\right)$$

Yechim qadamlari

7 omili.

$$7\left(w^{2}+6w-27\right)$$

Hisoblang: w^{2}+6w-27. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda w^{2}+aw+bw-27 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=6 ab=1\left(-27\right)=-27$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -27-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,27 -3,9$$

Har bir juftlik yigʻindisini hisoblang.

$$-1+27=26 -3+9=6$$

Yechim – 6 yigʻindisini beruvchi juftlik.

$$a=-3 b=9$$

w^{2}+6w-27 ni \left(w^{2}-3w\right)+\left(9w-27\right) sifatida qaytadan yozish.

$$\left(w^{2}-3w\right)+\left(9w-27\right)$$

Birinchi guruhda w ni va ikkinchi guruhda 9 ni faktordan chiqaring.

$$w\left(w-3\right)+9\left(w-3\right)$$

Distributiv funktsiyasidan foydalangan holda w-3 umumiy terminini chiqaring.

$$\left(w-3\right)\left(w+9\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$7\left(w-3\right)\left(w+9\right)$$

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.

$$7w^{2}+42w-189=0$$

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.

$$w=\frac{-42±\sqrt{42^{2}-4\times 7\left(-189\right)}}{2\times 7}$$

42 kvadratini chiqarish.

$$w=\frac{-42±\sqrt{1764-4\times 7\left(-189\right)}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$w=\frac{-42±\sqrt{1764-28\left(-189\right)}}{2\times 7}$$

-28 ni -189 marotabaga ko'paytirish.

$$w=\frac{-42±\sqrt{1764+5292}}{2\times 7}$$

1764 ni 5292 ga qo'shish.

$$w=\frac{-42±\sqrt{7056}}{2\times 7}$$

7056 ning kvadrat ildizini chiqarish.

$$w=\frac{-42±84}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$w=\frac{-42±84}{14}$$

w=\frac{-42±84}{14} tenglamasini yeching, bunda ± musbat. -42 ni 84 ga qo'shish.

$$w=\frac{42}{14}$$

42 ni 14 ga bo'lish.

$$w=3$$

w=\frac{-42±84}{14} tenglamasini yeching, bunda ± manfiy. -42 dan 84 ni ayirish.

$$w=-\frac{126}{14}$$

-126 ni 14 ga bo'lish.

$$w=-9$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 3 ga va x_{2} uchun -9 ga bo‘ling.

$$7w^{2}+42w-189=7\left(w-3\right)\left(w-\left(-9\right)\right)$$

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

$$7w^{2}+42w-189=7\left(w-3\right)\left(w+9\right)$$

Baholash

$$7\left(w-3\right)\left(w+9\right)$$