2x^2-8x-24= eching

$$2 x ^ { 2 } - 8 x - 24 =$$

Omil

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

Yechim qadamlari

2 omili.

$$2\left(x^{2}-4x-12\right)$$

Hisoblang: x^{2}-4x-12. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-12 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-4 ab=1\left(-12\right)=-12$$

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 – -4 yigʻindisini beruvchi juftlik.

$$a=-6 b=2$$

x^{2}-4x-12 ni \left(x^{2}-6x\right)+\left(2x-12\right) sifatida qaytadan yozish.

$$\left(x^{2}-6x\right)+\left(2x-12\right)$$

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

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

Distributiv funktsiyasidan foydalangan holda x-6 umumiy terminini chiqaring.

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

Toʻliq ajratilgan ifodani qaytadan yozing.

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

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.

$$2x^{2}-8x-24=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-24\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-24\right)}}{2\times 2}$$

-8 ni -24 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+192}}{2\times 2}$$

64 ni 192 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{256}}{2\times 2}$$

256 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±16}{2\times 2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±16}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{8±16}{4}$$

x=\frac{8±16}{4} tenglamasini yeching, bunda ± musbat. 8 ni 16 ga qo'shish.

$$x=\frac{24}{4}$$

24 ni 4 ga bo'lish.

$$x=6$$

x=\frac{8±16}{4} tenglamasini yeching, bunda ± manfiy. 8 dan 16 ni ayirish.

$$x=-\frac{8}{4}$$

-8 ni 4 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 6 ga va x_{2} uchun -2 ga bo‘ling.

$$2x^{2}-8x-24=2\left(x-6\right)\left(x-\left(-2\right)\right)$$

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

$$2x^{2}-8x-24=2\left(x-6\right)\left(x+2\right)$$

Baholash

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