5x^2-6x=0 eching

$$5 { x }^{ 2 } -6x=0$$

x uchun yechish

$$x = \frac{6}{5} = 1\frac{1}{5} = 1,2$$

$$x=0$$

Faktorlash qadamlari

x omili.

$$x\left(5x-6\right)=0$$

Tenglamani yechish uchun x=0 va 5x-6=0 ni yeching.

$$x=0 x=\frac{6}{5}$$

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.

$$5x^{2}-6x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 5 ni a, -6 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 5}$$

\left(-6\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±6}{2\times 5}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±6}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{6±6}{10}$$

x=\frac{6±6}{10} tenglamasini yeching, bunda ± musbat. 6 ni 6 ga qo'shish.

$$x=\frac{12}{10}$$

\frac{12}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{6}{5}$$

x=\frac{6±6}{10} tenglamasini yeching, bunda ± manfiy. 6 dan 6 ni ayirish.

$$x=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{6}{5} x=0$$

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.

$$5x^{2}-6x=0$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-6x}{5}=\frac{0}{5}$$

5 ga bo'lish 5 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{6}{5}x=\frac{0}{5}$$

0 ni 5 ga bo'lish.

$$x^{2}-\frac{6}{5}x=0$$

-\frac{6}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{5} olish uchun. Keyin, -\frac{3}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{6}{5}x+\left(-\frac{3}{5}\right)^{2}=\left(-\frac{3}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{5} kvadratini chiqarish.

$$x^{2}-\frac{6}{5}x+\frac{9}{25}=\frac{9}{25}$$

x^{2}-\frac{6}{5}x+\frac{9}{25} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{5}\right)^{2}=\frac{9}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{5}\right)^{2}}=\sqrt{\frac{9}{25}}$$

Qisqartirish.

$$x-\frac{3}{5}=\frac{3}{5} x-\frac{3}{5}=-\frac{3}{5}$$

\frac{3}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{6}{5} x=0$$