-3x^2-39x-36 eching

$$-3 { x }^{ 2 } -39x-36$$

Omil

$$-3\left(x+1\right)\left(x+12\right)$$

Yechim qadamlari

3 omili.

$$3\left(-x^{2}-13x-12\right)$$

Hisoblang: -x^{2}-13x-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.

$$a+b=-13 ab=-\left(-12\right)=12$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. 12-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,-12 -2,-6 -3,-4$$

Har bir juftlik yigʻindisini hisoblang.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

Yechim – -13 yigʻindisini beruvchi juftlik.

$$a=-1 b=-12$$

-x^{2}-13x-12 ni \left(-x^{2}-x\right)+\left(-12x-12\right) sifatida qaytadan yozish.

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

Birinchi guruhda x ni va ikkinchi guruhda 12 ni faktordan chiqaring.

$$x\left(-x-1\right)+12\left(-x-1\right)$$

Distributiv funktsiyasidan foydalangan holda -x-1 umumiy terminini chiqaring.

$$\left(-x-1\right)\left(x+12\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$3\left(-x-1\right)\left(x+12\right)$$

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.

$$-3x^{2}-39x-36=0$$

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.

$$x=\frac{-\left(-39\right)±\sqrt{\left(-39\right)^{2}-4\left(-3\right)\left(-36\right)}}{2\left(-3\right)}$$

-39 kvadratini chiqarish.

$$x=\frac{-\left(-39\right)±\sqrt{1521-4\left(-3\right)\left(-36\right)}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-39\right)±\sqrt{1521+12\left(-36\right)}}{2\left(-3\right)}$$

12 ni -36 marotabaga ko'paytirish.

$$x=\frac{-\left(-39\right)±\sqrt{1521-432}}{2\left(-3\right)}$$

1521 ni -432 ga qo'shish.

$$x=\frac{-\left(-39\right)±\sqrt{1089}}{2\left(-3\right)}$$

1089 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-39\right)±33}{2\left(-3\right)}$$

-39 ning teskarisi 39 ga teng.

$$x=\frac{39±33}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{39±33}{-6}$$

x=\frac{39±33}{-6} tenglamasini yeching, bunda ± musbat. 39 ni 33 ga qo'shish.

$$x=\frac{72}{-6}$$

72 ni -6 ga bo'lish.

$$x=-12$$

x=\frac{39±33}{-6} tenglamasini yeching, bunda ± manfiy. 39 dan 33 ni ayirish.

$$x=\frac{6}{-6}$$

6 ni -6 ga bo'lish.

$$x=-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -12 ga va x_{2} uchun -1 ga bo‘ling.

$$-3x^{2}-39x-36=-3\left(x-\left(-12\right)\right)\left(x-\left(-1\right)\right)$$

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

$$-3x^{2}-39x-36=-3\left(x+12\right)\left(x+1\right)$$

Baholash

$$-3\left(x+1\right)\left(x+12\right)$$