5x^2=4x eching

$$5 x ^ { 2 } = 4 x$$

x uchun yechish

$$x=\frac{4}{5}=0,8$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 4x ni ayirish.

$$5x^{2}-4x=0$$

x omili.

$$x\left(5x-4\right)=0$$

Tenglamani yechish uchun x=0 va 5x-4=0 ni yeching.

$$x=0 x=\frac{4}{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 4x ni ayirish.

$$5x^{2}-4x=0$$

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

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2\times 5}$$

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

$$x=\frac{-\left(-4\right)±4}{2\times 5}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{4±4}{10}$$

x=\frac{4±4}{10} tenglamasini yeching, bunda ± musbat. 4 ni 4 ga qo'shish.

$$x=\frac{8}{10}$$

\frac{8}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{4}{5}$$

x=\frac{4±4}{10} tenglamasini yeching, bunda ± manfiy. 4 dan 4 ni ayirish.

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

0 ni 10 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=\frac{4}{5} x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 4x ni ayirish.

$$5x^{2}-4x=0$$

Ikki tarafini 5 ga bo‘ling.

$$\frac{5x^{2}-4x}{5}=\frac{0}{5}$$

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

$$x^{2}-\frac{4}{5}x=\frac{0}{5}$$

0 ni 5 ga bo'lish.

$$x^{2}-\frac{4}{5}x=0$$

-\frac{4}{5} ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{2}{5} olish uchun. Keyin, -\frac{2}{5} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-\frac{4}{5}x+\left(-\frac{2}{5}\right)^{2}=\left(-\frac{2}{5}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{2}{5} kvadratini chiqarish.

$$x^{2}-\frac{4}{5}x+\frac{4}{25}=\frac{4}{25}$$

x^{2}-\frac{4}{5}x+\frac{4}{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.

$$\left(x-\frac{2}{5}\right)^{2}=\frac{4}{25}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{2}{5}\right)^{2}}=\sqrt{\frac{4}{25}}$$

Qisqartirish.

$$x-\frac{2}{5}=\frac{2}{5} x-\frac{2}{5}=-\frac{2}{5}$$

\frac{2}{5} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{4}{5} x=0$$