18n^2-909n eching

$$18 n ^ { 2 } - 909 n$$

Omil

$$9n\left(2n-101\right)$$

Yechim qadamlari

9 omili.

$$9\left(2n^{2}-101n\right)$$

Hisoblang: 2n^{2}-101n. n omili.

$$n\left(2n-101\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$9n\left(2n-101\right)$$

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.

$$18n^{2}-909n=0$$

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.

$$n=\frac{-\left(-909\right)±\sqrt{\left(-909\right)^{2}}}{2\times 18}$$

\left(-909\right)^{2} ning kvadrat ildizini chiqarish.

$$n=\frac{-\left(-909\right)±909}{2\times 18}$$

-909 ning teskarisi 909 ga teng.

$$n=\frac{909±909}{2\times 18}$$

2 ni 18 marotabaga ko'paytirish.

$$n=\frac{909±909}{36}$$

n=\frac{909±909}{36} tenglamasini yeching, bunda ± musbat. 909 ni 909 ga qo'shish.

$$n=\frac{1818}{36}$$

\frac{1818}{36} ulushini 18 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$n=\frac{101}{2}$$

n=\frac{909±909}{36} tenglamasini yeching, bunda ± manfiy. 909 dan 909 ni ayirish.

$$n=\frac{0}{36}$$

0 ni 36 ga bo'lish.

$$n=0$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{101}{2} ga va x_{2} uchun 0 ga bo‘ling.

$$18n^{2}-909n=18\left(n-\frac{101}{2}\right)n$$

Umumiy maxrajni topib va suratlarni ayirib \frac{101}{2} ni n dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$18n^{2}-909n=18\times \frac{2n-101}{2}n$$

18 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$18n^{2}-909n=9\left(2n-101\right)n$$

Baholash

$$9n\left(2n-101\right)$$