c/T=c/T*c/1 eching

$$\frac { c } { T } = \frac { c } { T } \times \frac { c } { 1 }$$

c uchun yechish

$$c=1$$

$$c=0\text{, }T\neq 0$$

Faktorlash qadamlari

Tenglamaning ikkala tarafini T ga ko'paytirish.

$$c=c\times \frac{c}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$c=cc$$

c^{2} hosil qilish uchun c va c ni ko'paytirish.

$$c=c^{2}$$

Ikkala tarafdan c^{2} ni ayirish.

$$c-c^{2}=0$$

c omili.

$$c\left(1-c\right)=0$$

Tenglamani yechish uchun c=0 va 1-c=0 ni yeching.

$$c=0 c=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tenglamaning ikkala tarafini T ga ko'paytirish.

$$c=c\times \frac{c}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$c=cc$$

c^{2} hosil qilish uchun c va c ni ko'paytirish.

$$c=c^{2}$$

Ikkala tarafdan c^{2} ni ayirish.

$$c-c^{2}=0$$

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.

$$-c^{2}+c=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, 1 ni b va 0 ni c bilan almashtiring.

$$c=\frac{-1±\sqrt{1^{2}}}{2\left(-1\right)}$$

1^{2} ning kvadrat ildizini chiqarish.

$$c=\frac{-1±1}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$c=\frac{-1±1}{-2}$$

c=\frac{-1±1}{-2} tenglamasini yeching, bunda ± musbat. -1 ni 1 ga qo'shish.

$$c=\frac{0}{-2}$$

0 ni -2 ga bo'lish.

$$c=0$$

c=\frac{-1±1}{-2} tenglamasini yeching, bunda ± manfiy. -1 dan 1 ni ayirish.

$$c=-\frac{2}{-2}$$

-2 ni -2 ga bo'lish.

$$c=1$$

Tenglama yechildi.

$$c=0 c=1$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafini T ga ko'paytirish.

$$c=c\times \frac{c}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$c=cc$$

c^{2} hosil qilish uchun c va c ni ko'paytirish.

$$c=c^{2}$$

Ikkala tarafdan c^{2} ni ayirish.

$$c-c^{2}=0$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-c^{2}+c=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-c^{2}+c}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$c^{2}+\frac{1}{-1}c=\frac{0}{-1}$$

1 ni -1 ga bo'lish.

$$c^{2}-c=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$c^{2}-c=0$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$c^{2}-c+\left(-\frac{1}{2}\right)^{2}=\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$c^{2}-c+\frac{1}{4}=\frac{1}{4}$$

c^{2}-c+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(c-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(c-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Qisqartirish.

$$c-\frac{1}{2}=\frac{1}{2} c-\frac{1}{2}=-\frac{1}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$c=1 c=0$$

T uchun yechish

$$T\neq 0$$

$$c=1\text{ or }c=0$$