7x^2=4x eching

$$7 x ^ { 2 } = 4 x$$

x uchun yechish

$$x=\frac{4}{7}\approx 0,571428571$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 4x ni ayirish.

$$7x^{2}-4x=0$$

x omili.

$$x\left(7x-4\right)=0$$

Tenglamani yechish uchun x=0 va 7x-4=0 ni yeching.

$$x=0 x=\frac{4}{7}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 4x ni ayirish.

$$7x^{2}-4x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, -4 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2\times 7}$$

\left(-4\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±4}{2\times 7}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{4±4}{14}$$

x=\frac{4±4}{14} tenglamasini yeching, bunda ± musbat. 4 ni 4 ga qo'shish.

$$x=\frac{8}{14}$$

\frac{8}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{4}{7}$$

x=\frac{4±4}{14} tenglamasini yeching, bunda ± manfiy. 4 dan 4 ni ayirish.

$$x=\frac{0}{14}$$

0 ni 14 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{4}{7} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 4x ni ayirish.

$$7x^{2}-4x=0$$

Ikki tarafini 7 ga bo‘ling.

$$\frac{7x^{2}-4x}{7}=\frac{0}{7}$$

7 ga bo'lish 7 ga ko'paytirishni bekor qiladi.

$$x^{2}-\frac{4}{7}x=\frac{0}{7}$$

0 ni 7 ga bo'lish.

$$x^{2}-\frac{4}{7}x=0$$

-\frac{4}{7} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{2}{7} olish uchun. Keyin, -\frac{2}{7} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{4}{7}x+\left(-\frac{2}{7}\right)^{2}=\left(-\frac{2}{7}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{2}{7} kvadratini chiqarish.

$$x^{2}-\frac{4}{7}x+\frac{4}{49}=\frac{4}{49}$$

x^{2}-\frac{4}{7}x+\frac{4}{49} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{2}{7}\right)^{2}=\frac{4}{49}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{2}{7}\right)^{2}}=\sqrt{\frac{4}{49}}$$

Qisqartirish.

$$x-\frac{2}{7}=\frac{2}{7} x-\frac{2}{7}=-\frac{2}{7}$$

\frac{2}{7} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{4}{7} x=0$$