6x^2-18x-60= eching

$$6 x ^ { 2 } - 18 x - 60 =$$

Omil

$$6\left(x-5\right)\left(x+2\right)$$

Yechim qadamlari

6 omili.

$$6\left(x^{2}-3x-10\right)$$

Hisoblang: x^{2}-3x-10. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-10 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-3 ab=1\left(-10\right)=-10$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -10-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-10 2,-5$$

Har bir juftlik yigʻindisini hisoblang.

$$1-10=-9 2-5=-3$$

Yechim – -3 yigʻindisini beruvchi juftlik.

$$a=-5 b=2$$

x^{2}-3x-10 ni \left(x^{2}-5x\right)+\left(2x-10\right) sifatida qaytadan yozish.

$$\left(x^{2}-5x\right)+\left(2x-10\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 2 ni faktordan chiqaring.

$$x\left(x-5\right)+2\left(x-5\right)$$

Distributiv funktsiyasidan foydalangan holda x-5 umumiy terminini chiqaring.

$$\left(x-5\right)\left(x+2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$6\left(x-5\right)\left(x+2\right)$$

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.

$$6x^{2}-18x-60=0$$

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.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 6\left(-60\right)}}{2\times 6}$$

-18 kvadratini chiqarish.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 6\left(-60\right)}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324-24\left(-60\right)}}{2\times 6}$$

-24 ni -60 marotabaga ko'paytirish.

$$x=\frac{-\left(-18\right)±\sqrt{324+1440}}{2\times 6}$$

324 ni 1440 ga qo'shish.

$$x=\frac{-\left(-18\right)±\sqrt{1764}}{2\times 6}$$

1764 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±42}{2\times 6}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±42}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$x=\frac{18±42}{12}$$

x=\frac{18±42}{12} tenglamasini yeching, bunda ± musbat. 18 ni 42 ga qo'shish.

$$x=\frac{60}{12}$$

60 ni 12 ga bo'lish.

$$x=5$$

x=\frac{18±42}{12} tenglamasini yeching, bunda ± manfiy. 18 dan 42 ni ayirish.

$$x=-\frac{24}{12}$$

-24 ni 12 ga bo'lish.

$$x=-2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 5 ga va x_{2} uchun -2 ga bo‘ling.

$$6x^{2}-18x-60=6\left(x-5\right)\left(x-\left(-2\right)\right)$$

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

$$6x^{2}-18x-60=6\left(x-5\right)\left(x+2\right)$$

Baholash

$$6\left(x-5\right)\left(x+2\right)$$