018+8x^2-18x=0 eching

$$018 + 8 x ^ { 2 } - 18 x = 0$$

x uchun yechish

$$x = \frac{9}{4} = 2\frac{1}{4} = 2,25$$

$$x=0$$

Faktorlash qadamlari

0 hosil qilish uchun 0 va 18 ni ko'paytirish.

$$0+8x^{2}-18x=0$$

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

$$8x^{2}-18x=0$$

x omili.

$$x\left(8x-18\right)=0$$

Tenglamani yechish uchun x=0 va 8x-18=0 ni yeching.

$$x=0 x=\frac{9}{4}$$

Kvadrat tenglamalaridan foydalanish qoidalari

0 hosil qilish uchun 0 va 18 ni ko'paytirish.

$$0+8x^{2}-18x=0$$

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

$$8x^{2}-18x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, -18 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2\times 8}$$

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

$$x=\frac{-\left(-18\right)±18}{2\times 8}$$

-18 ning teskarisi 18 ga teng.

$$x=\frac{18±18}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{18±18}{16}$$

x=\frac{18±18}{16} tenglamasini yeching, bunda ± musbat. 18 ni 18 ga qo'shish.

$$x=\frac{36}{16}$$

\frac{36}{16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{9}{4}$$

x=\frac{18±18}{16} tenglamasini yeching, bunda ± manfiy. 18 dan 18 ni ayirish.

$$x=\frac{0}{16}$$

0 ni 16 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{9}{4} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

0 hosil qilish uchun 0 va 18 ni ko'paytirish.

$$0+8x^{2}-18x=0$$

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

$$8x^{2}-18x=0$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8x^{2}-18x}{8}=\frac{0}{8}$$

8 ga bo'lish 8 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{18}{8}\right)x=\frac{0}{8}$$

\frac{-18}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x^{2}-\frac{9}{4}x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x^{2}-\frac{9}{4}x=0$$

-\frac{9}{4} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{9}{8} olish uchun. Keyin, -\frac{9}{8} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{9}{4}x+\left(-\frac{9}{8}\right)^{2}=\left(-\frac{9}{8}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{9}{8} kvadratini chiqarish.

$$x^{2}-\frac{9}{4}x+\frac{81}{64}=\frac{81}{64}$$

x^{2}-\frac{9}{4}x+\frac{81}{64} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{9}{8}\right)^{2}=\frac{81}{64}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{9}{8}\right)^{2}}=\sqrt{\frac{81}{64}}$$

Qisqartirish.

$$x-\frac{9}{8}=\frac{9}{8} x-\frac{9}{8}=-\frac{9}{8}$$

\frac{9}{8} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{9}{4} x=0$$