15K^2-3K=0 eching

$$15 K ^ { 2 } - 3 K = 0$$

K uchun yechish

$$K=\frac{1}{5}=0,2$$

$$K=0$$

Faktorlash qadamlari

K omili.

$$K\left(15K-3\right)=0$$

Tenglamani yechish uchun K=0 va 15K-3=0 ni yeching.

$$K=0 K=\frac{1}{5}$$

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.

$$15K^{2}-3K=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 15 ni a, -3 ni b va 0 ni c bilan almashtiring.

$$K=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 15}$$

\left(-3\right)^{2} ning kvadrat ildizini chiqarish.

$$K=\frac{-\left(-3\right)±3}{2\times 15}$$

-3 ning teskarisi 3 ga teng.

$$K=\frac{3±3}{2\times 15}$$

2 ni 15 marotabaga ko'paytirish.

$$K=\frac{3±3}{30}$$

K=\frac{3±3}{30} tenglamasini yeching, bunda ± musbat. 3 ni 3 ga qo'shish.

$$K=\frac{6}{30}$$

\frac{6}{30} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$K=\frac{1}{5}$$

K=\frac{3±3}{30} tenglamasini yeching, bunda ± manfiy. 3 dan 3 ni ayirish.

$$K=\frac{0}{30}$$

0 ni 30 ga bo'lish.

$$K=0$$

Tenglama yechildi.

$$K=\frac{1}{5} K=0$$

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.

$$15K^{2}-3K=0$$

Ikki tarafini 15 ga bo‘ling.

$$\frac{15K^{2}-3K}{15}=\frac{0}{15}$$

15 ga bo'lish 15 ga ko'paytirishni bekor qiladi.

$$K^{2}+\left(-\frac{3}{15}\right)K=\frac{0}{15}$$

\frac{-3}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$K^{2}-\frac{1}{5}K=\frac{0}{15}$$

0 ni 15 ga bo'lish.

$$K^{2}-\frac{1}{5}K=0$$

-\frac{1}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{10} olish uchun. Keyin, -\frac{1}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$K^{2}-\frac{1}{5}K+\left(-\frac{1}{10}\right)^{2}=\left(-\frac{1}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{10} kvadratini chiqarish.

$$K^{2}-\frac{1}{5}K+\frac{1}{100}=\frac{1}{100}$$

K^{2}-\frac{1}{5}K+\frac{1}{100} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(K-\frac{1}{10}\right)^{2}=\frac{1}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(K-\frac{1}{10}\right)^{2}}=\sqrt{\frac{1}{100}}$$

Qisqartirish.

$$K-\frac{1}{10}=\frac{1}{10} K-\frac{1}{10}=-\frac{1}{10}$$

\frac{1}{10} ni tenglamaning ikkala tarafiga qo'shish.

$$K=\frac{1}{5} K=0$$