6w^2-66w-72 eching

$$6 w ^ { 2 } - 66 w - 72$$

Omil

$$6\left(w-12\right)\left(w+1\right)$$

Yechim qadamlari

6 omili.

$$6\left(w^{2}-11w-12\right)$$

Hisoblang: w^{2}-11w-12. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda w^{2}+aw+bw-12 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-11 ab=1\left(-12\right)=-12$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -12-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-12 2,-6 3,-4$$

Har bir juftlik yigʻindisini hisoblang.

$$1-12=-11 2-6=-4 3-4=-1$$

Yechim – -11 yigʻindisini beruvchi juftlik.

$$a=-12 b=1$$

w^{2}-11w-12 ni \left(w^{2}-12w\right)+\left(w-12\right) sifatida qaytadan yozish.

$$\left(w^{2}-12w\right)+\left(w-12\right)$$

w^{2}-12w ichida w ni ajrating.

$$w\left(w-12\right)+w-12$$

Distributiv funktsiyasidan foydalangan holda w-12 umumiy terminini chiqaring.

$$\left(w-12\right)\left(w+1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$6\left(w-12\right)\left(w+1\right)$$

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.

$$6w^{2}-66w-72=0$$

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.

$$w=\frac{-\left(-66\right)±\sqrt{\left(-66\right)^{2}-4\times 6\left(-72\right)}}{2\times 6}$$

-66 kvadratini chiqarish.

$$w=\frac{-\left(-66\right)±\sqrt{4356-4\times 6\left(-72\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$w=\frac{-\left(-66\right)±\sqrt{4356-24\left(-72\right)}}{2\times 6}$$

-24 ni -72 marotabaga ko'paytirish.

$$w=\frac{-\left(-66\right)±\sqrt{4356+1728}}{2\times 6}$$

4356 ni 1728 ga qo'shish.

$$w=\frac{-\left(-66\right)±\sqrt{6084}}{2\times 6}$$

6084 ning kvadrat ildizini chiqarish.

$$w=\frac{-\left(-66\right)±78}{2\times 6}$$

-66 ning teskarisi 66 ga teng.

$$w=\frac{66±78}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$w=\frac{66±78}{12}$$

w=\frac{66±78}{12} tenglamasini yeching, bunda ± musbat. 66 ni 78 ga qo'shish.

$$w=\frac{144}{12}$$

144 ni 12 ga bo'lish.

$$w=12$$

w=\frac{66±78}{12} tenglamasini yeching, bunda ± manfiy. 66 dan 78 ni ayirish.

$$w=-\frac{12}{12}$$

-12 ni 12 ga bo'lish.

$$w=-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 12 ga va x_{2} uchun -1 ga bo‘ling.

$$6w^{2}-66w-72=6\left(w-12\right)\left(w-\left(-1\right)\right)$$

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

$$6w^{2}-66w-72=6\left(w-12\right)\left(w+1\right)$$

Baholash

$$6\left(w-12\right)\left(w+1\right)$$