c^2-5c=0 eching

$$c ^ { 2 } - 5 c = 0$$

c uchun yechish

$$c=5$$

$$c=0$$

Faktorlash qadamlari

c omili.

$$c\left(c-5\right)=0$$

Tenglamani yechish uchun c=0 va c-5=0 ni yeching.

$$c=0 c=5$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

$$c^{2}-5c=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -5 ni b va 0 ni c bilan almashtiring.

$$c=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}}}{2}$$

\left(-5\right)^{2} ning kvadrat ildizini chiqarish.

$$c=\frac{-\left(-5\right)±5}{2}$$

-5 ning teskarisi 5 ga teng.

$$c=\frac{5±5}{2}$$

c=\frac{5±5}{2} tenglamasini yeching, bunda ± musbat. 5 ni 5 ga qo'shish.

$$c=\frac{10}{2}$$

10 ni 2 ga bo'lish.

$$c=5$$

c=\frac{5±5}{2} tenglamasini yeching, bunda ± manfiy. 5 dan 5 ni ayirish.

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

0 ni 2 ga bo'lish.

$$c=0$$

Tenglama yechildi.

$$c=5 c=0$$

Kvadratni yakunlash bo'yicha qadamlar

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

$$c^{2}-5c=0$$

-5 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{5}{2} olish uchun. Keyin, -\frac{5}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$c^{2}-5c+\left(-\frac{5}{2}\right)^{2}=\left(-\frac{5}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{5}{2} kvadratini chiqarish.

$$c^{2}-5c+\frac{25}{4}=\frac{25}{4}$$

c^{2}-5c+\frac{25}{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.

$$\left(c-\frac{5}{2}\right)^{2}=\frac{25}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(c-\frac{5}{2}\right)^{2}}=\sqrt{\frac{25}{4}}$$

Qisqartirish.

$$c-\frac{5}{2}=\frac{5}{2} c-\frac{5}{2}=-\frac{5}{2}$$

\frac{5}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$c=5 c=0$$