x^2=2x eching

$$x ^ { 2 } = 2 x$$

x uchun yechish

$$x=2$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 2x ni ayirish.

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

x omili.

$$x\left(x-2\right)=0$$

Tenglamani yechish uchun x=0 va x-2=0 ni yeching.

$$x=0 x=2$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x ni ayirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -2 ni b va 0 ni c bilan almashtiring.

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

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

$$x=\frac{-\left(-2\right)±2}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2}{2}$$

x=\frac{2±2}{2} tenglamasini yeching, bunda ± musbat. 2 ni 2 ga qo'shish.

$$x=\frac{4}{2}$$

4 ni 2 ga bo'lish.

$$x=2$$

x=\frac{2±2}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 2 ni ayirish.

$$x=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=2 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish.

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

-2 ni bo‘lish, x shartining koeffitsienti, 2 ga -1 olish uchun. Keyin, -1 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-2x+1=1$$

x^{2}-2x+1 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-1\right)^{2}=1$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{1}$$

Qisqartirish.

$$x-1=1 x-1=-1$$

1 ni tenglamaning ikkala tarafiga qo'shish.

$$x=2 x=0$$