x^2-32x-2448 eching

$$x ^ { 2 } - 32 x - 2448$$

Omil

$$\left(x-68\right)\left(x+36\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-2448 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-32 ab=1\left(-2448\right)=-2448$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -2448-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-2448 2,-1224 3,-816 4,-612 6,-408 8,-306 9,-272 12,-204 16,-153 17,-144 18,-136 24,-102 34,-72 36,-68 48,-51$$

Har bir juftlik yigʻindisini hisoblang.

$$1-2448=-2447 2-1224=-1222 3-816=-813 4-612=-608 6-408=-402 8-306=-298 9-272=-263 12-204=-192 16-153=-137 17-144=-127 18-136=-118 24-102=-78 34-72=-38 36-68=-32 48-51=-3$$

Yechim – -32 yigʻindisini beruvchi juftlik.

$$a=-68 b=36$$

x^{2}-32x-2448 ni \left(x^{2}-68x\right)+\left(36x-2448\right) sifatida qaytadan yozish.

$$\left(x^{2}-68x\right)+\left(36x-2448\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 36 ni faktordan chiqaring.

$$x\left(x-68\right)+36\left(x-68\right)$$

Distributiv funktsiyasidan foydalangan holda x-68 umumiy terminini chiqaring.

$$\left(x-68\right)\left(x+36\right)$$

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.

$$x^{2}-32x-2448=0$$

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.

$$x=\frac{-\left(-32\right)±\sqrt{\left(-32\right)^{2}-4\left(-2448\right)}}{2}$$

-32 kvadratini chiqarish.

$$x=\frac{-\left(-32\right)±\sqrt{1024-4\left(-2448\right)}}{2}$$

-4 ni -2448 marotabaga ko'paytirish.

$$x=\frac{-\left(-32\right)±\sqrt{1024+9792}}{2}$$

1024 ni 9792 ga qo'shish.

$$x=\frac{-\left(-32\right)±\sqrt{10816}}{2}$$

10816 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-32\right)±104}{2}$$

-32 ning teskarisi 32 ga teng.

$$x=\frac{32±104}{2}$$

x=\frac{32±104}{2} tenglamasini yeching, bunda ± musbat. 32 ni 104 ga qo'shish.

$$x=\frac{136}{2}$$

136 ni 2 ga bo'lish.

$$x=68$$

x=\frac{32±104}{2} tenglamasini yeching, bunda ± manfiy. 32 dan 104 ni ayirish.

$$x=-\frac{72}{2}$$

-72 ni 2 ga bo'lish.

$$x=-36$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 68 ga va x_{2} uchun -36 ga bo‘ling.

$$x^{2}-32x-2448=\left(x-68\right)\left(x-\left(-36\right)\right)$$

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

$$x^{2}-32x-2448=\left(x-68\right)\left(x+36\right)$$

Baholash

$$\left(x-68\right)\left(x+36\right)$$