10x^2-18x+0=0 eching

$$10 { x }^{ 2 } -18x+0 = 0$$

x uchun yechish

$$x = \frac{9}{5} = 1\frac{4}{5} = 1,8$$

$$x=0$$

Faktorlash qadamlari

Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$10x^{2}-18x=0$$

x omili.

$$x\left(10x-18\right)=0$$

Tenglamani yechish uchun x=0 va 10x-18=0 ni yeching.

$$x=0 x=\frac{9}{5}$$

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.

$$10x^{2}-18x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 10 ni a, -18 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2\times 10}$$

\left(-18\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-18\right)±18}{2\times 10}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±18}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$x=\frac{18±18}{20}$$

x=\frac{18±18}{20} tenglamasini yeching, bunda ± musbat. 18 ni 18 ga qo'shish.

$$x=\frac{36}{20}$$

\frac{36}{20} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{9}{5}$$

x=\frac{18±18}{20} tenglamasini yeching, bunda ± manfiy. 18 dan 18 ni ayirish.

$$x=\frac{0}{20}$$

0 ni 20 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{9}{5} x=0$$

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.

$$10x^{2}-18x=0$$

Ikki tarafini 10 ga bo‘ling.

$$\frac{10x^{2}-18x}{10}=\frac{0}{10}$$

10 ga bo'lish 10 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{18}{10}\right)x=\frac{0}{10}$$

\frac{-18}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{9}{5}x=\frac{0}{10}$$

0 ni 10 ga bo'lish.

$$x^{2}-\frac{9}{5}x=0$$

-\frac{9}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{10} olish uchun. Keyin, -\frac{9}{10} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{9}{5}x+\left(-\frac{9}{10}\right)^{2}=\left(-\frac{9}{10}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{10} kvadratini chiqarish.

$$x^{2}-\frac{9}{5}x+\frac{81}{100}=\frac{81}{100}$$

x^{2}-\frac{9}{5}x+\frac{81}{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.

$$\left(x-\frac{9}{10}\right)^{2}=\frac{81}{100}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{10}\right)^{2}}=\sqrt{\frac{81}{100}}$$

Qisqartirish.

$$x-\frac{9}{10}=\frac{9}{10} x-\frac{9}{10}=-\frac{9}{10}$$

\frac{9}{10} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{9}{5} x=0$$