x^2-30x-2800 eching

$$x ^ { 2 } - 30 x - 2800$$

Omil

$$\left(x-70\right)\left(x+40\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-2800 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-30 ab=1\left(-2800\right)=-2800$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -2800-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-2800 2,-1400 4,-700 5,-560 7,-400 8,-350 10,-280 14,-200 16,-175 20,-140 25,-112 28,-100 35,-80 40,-70 50,-56$$

Har bir juftlik yigʻindisini hisoblang.

$$1-2800=-2799 2-1400=-1398 4-700=-696 5-560=-555 7-400=-393 8-350=-342 10-280=-270 14-200=-186 16-175=-159 20-140=-120 25-112=-87 28-100=-72 35-80=-45 40-70=-30 50-56=-6$$

Yechim – -30 yigʻindisini beruvchi juftlik.

$$a=-70 b=40$$

x^{2}-30x-2800 ni \left(x^{2}-70x\right)+\left(40x-2800\right) sifatida qaytadan yozish.

$$\left(x^{2}-70x\right)+\left(40x-2800\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 40 ni faktordan chiqaring.

$$x\left(x-70\right)+40\left(x-70\right)$$

Distributiv funktsiyasidan foydalangan holda x-70 umumiy terminini chiqaring.

$$\left(x-70\right)\left(x+40\right)$$

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.

$$x^{2}-30x-2800=0$$

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.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}-4\left(-2800\right)}}{2}$$

-30 kvadratini chiqarish.

$$x=\frac{-\left(-30\right)±\sqrt{900-4\left(-2800\right)}}{2}$$

-4 ni -2800 marotabaga ko'paytirish.

$$x=\frac{-\left(-30\right)±\sqrt{900+11200}}{2}$$

900 ni 11200 ga qo'shish.

$$x=\frac{-\left(-30\right)±\sqrt{12100}}{2}$$

12100 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-30\right)±110}{2}$$

-30 ning teskarisi 30 ga teng.

$$x=\frac{30±110}{2}$$

x=\frac{30±110}{2} tenglamasini yeching, bunda ± musbat. 30 ni 110 ga qo'shish.

$$x=\frac{140}{2}$$

140 ni 2 ga bo'lish.

$$x=70$$

x=\frac{30±110}{2} tenglamasini yeching, bunda ± manfiy. 30 dan 110 ni ayirish.

$$x=-\frac{80}{2}$$

-80 ni 2 ga bo'lish.

$$x=-40$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 70 ga va x_{2} uchun -40 ga bo‘ling.

$$x^{2}-30x-2800=\left(x-70\right)\left(x-\left(-40\right)\right)$$

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

$$x^{2}-30x-2800=\left(x-70\right)\left(x+40\right)$$

Baholash

$$\left(x-70\right)\left(x+40\right)$$