x^2-2x-80 eching

$$x ^ { 2 } - 2 x - 80$$

Omil

$$\left(x-10\right)\left(x+8\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-80 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=1\left(-80\right)=-80$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -80-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-80 2,-40 4,-20 5,-16 8,-10$$

Har bir juftlik yigʻindisini hisoblang.

$$1-80=-79 2-40=-38 4-20=-16 5-16=-11 8-10=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$a=-10 b=8$$

x^{2}-2x-80 ni \left(x^{2}-10x\right)+\left(8x-80\right) sifatida qaytadan yozish.

$$\left(x^{2}-10x\right)+\left(8x-80\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 8 ni faktordan chiqaring.

$$x\left(x-10\right)+8\left(x-10\right)$$

Distributiv funktsiyasidan foydalangan holda x-10 umumiy terminini chiqaring.

$$\left(x-10\right)\left(x+8\right)$$

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.

$$x^{2}-2x-80=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-80\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-80\right)}}{2}$$

-4 ni -80 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+320}}{2}$$

4 ni 320 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{324}}{2}$$

324 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±18}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±18}{2}$$

x=\frac{2±18}{2} tenglamasini yeching, bunda ± musbat. 2 ni 18 ga qo'shish.

$$x=\frac{20}{2}$$

20 ni 2 ga bo'lish.

$$x=10$$

x=\frac{2±18}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 18 ni ayirish.

$$x=-\frac{16}{2}$$

-16 ni 2 ga bo'lish.

$$x=-8$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 10 ga va x_{2} uchun -8 ga bo‘ling.

$$x^{2}-2x-80=\left(x-10\right)\left(x-\left(-8\right)\right)$$

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

$$x^{2}-2x-80=\left(x-10\right)\left(x+8\right)$$

Baholash

$$\left(x-10\right)\left(x+8\right)$$