8x^2=3x eching

$$8 x ^ { 2 } = 3 x$$

x uchun yechish

$$x=\frac{3}{8}=0,375$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 3x ni ayirish.

$$8x^{2}-3x=0$$

x omili.

$$x\left(8x-3\right)=0$$

Tenglamani yechish uchun x=0 va 8x-3=0 ni yeching.

$$x=0 x=\frac{3}{8}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 3x ni ayirish.

$$8x^{2}-3x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 8 ni a, -3 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 8}$$

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

$$x=\frac{-\left(-3\right)±3}{2\times 8}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±3}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$x=\frac{3±3}{16}$$

x=\frac{3±3}{16} tenglamasini yeching, bunda ± musbat. 3 ni 3 ga qo'shish.

$$x=\frac{6}{16}$$

\frac{6}{16} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{3}{8}$$

x=\frac{3±3}{16} tenglamasini yeching, bunda ± manfiy. 3 dan 3 ni ayirish.

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

0 ni 16 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{3}{8} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 3x ni ayirish.

$$8x^{2}-3x=0$$

Ikki tarafini 8 ga bo‘ling.

$$\frac{8x^{2}-3x}{8}=\frac{0}{8}$$

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

$$x^{2}-\frac{3}{8}x=\frac{0}{8}$$

0 ni 8 ga bo'lish.

$$x^{2}-\frac{3}{8}x=0$$

-\frac{3}{8} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{16} olish uchun. Keyin, -\frac{3}{16} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{3}{8}x+\left(-\frac{3}{16}\right)^{2}=\left(-\frac{3}{16}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{16} kvadratini chiqarish.

$$x^{2}-\frac{3}{8}x+\frac{9}{256}=\frac{9}{256}$$

x^{2}-\frac{3}{8}x+\frac{9}{256} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{16}\right)^{2}=\frac{9}{256}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{16}\right)^{2}}=\sqrt{\frac{9}{256}}$$

Qisqartirish.

$$x-\frac{3}{16}=\frac{3}{16} x-\frac{3}{16}=-\frac{3}{16}$$

\frac{3}{16} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3}{8} x=0$$