(x-3)^2=9 eching

$$( x - 3 ) ^ { 2 } = 9$$

x uchun yechish

$$x=6$$

$$x=0$$

Faktorlash qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-6x+9=9$$

Ikkala tarafdan 9 ni ayirish.

$$x^{2}-6x+9-9=0$$

0 olish uchun 9 dan 9 ni ayirish.

$$x^{2}-6x=0$$

x omili.

$$x\left(x-6\right)=0$$

Tenglamani yechish uchun x=0 va x-6=0 ni yeching.

$$x=0 x=6$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-3\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-6x+9=9$$

Ikkala tarafdan 9 ni ayirish.

$$x^{2}-6x+9-9=0$$

0 olish uchun 9 dan 9 ni ayirish.

$$x^{2}-6x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -6 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2}$$

\left(-6\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±6}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±6}{2}$$

x=\frac{6±6}{2} tenglamasini yeching, bunda ± musbat. 6 ni 6 ga qo'shish.

$$x=\frac{12}{2}$$

12 ni 2 ga bo'lish.

$$x=6$$

x=\frac{6±6}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 6 ni ayirish.

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

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=6 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

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

Qisqartirish.

$$x-3=3 x-3=-3$$

3 ni tenglamaning ikkala tarafiga qo'shish.

$$x=6 x=0$$