(x-2)^2-4=0 eching

$$( x - 2 ) ^ { 2 } - 4 = 0$$

x uchun yechish

$$x=4$$

$$x=0$$

Faktorlash qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

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

0 olish uchun 4 dan 4 ni ayirish.

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

x omili.

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

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

$$x=0 x=4$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

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

0 olish uchun 4 dan 4 ni ayirish.

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

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

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

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

$$x=\frac{-\left(-4\right)±4}{2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±4}{2}$$

x=\frac{4±4}{2} tenglamasini yeching, bunda ± musbat. 4 ni 4 ga qo'shish.

$$x=\frac{8}{2}$$

8 ni 2 ga bo'lish.

$$x=4$$

x=\frac{4±4}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 4 ni ayirish.

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

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=4 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-2\right)^{2} kengaytirilishi uchun ishlating.

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

0 olish uchun 4 dan 4 ni ayirish.

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

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

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

-2 kvadratini chiqarish.

$$x^{2}-4x+4=4$$

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

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

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-2=2 x-2=-2$$

2 ni tenglamaning ikkala tarafiga qo'shish.

$$x=4 x=0$$