(x-4)^2=16 eching

$$( x - 4 ) ^ { 2 } = 16$$

x uchun yechish

$$x=8$$

$$x=0$$

Faktorlash qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-4\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-8x+16=16$$

Ikkala tarafdan 16 ni ayirish.

$$x^{2}-8x+16-16=0$$

0 olish uchun 16 dan 16 ni ayirish.

$$x^{2}-8x=0$$

x omili.

$$x\left(x-8\right)=0$$

Tenglamani yechish uchun x=0 va x-8=0 ni yeching.

$$x=0 x=8$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(x-4\right)^{2} kengaytirilishi uchun ishlating.

$$x^{2}-8x+16=16$$

Ikkala tarafdan 16 ni ayirish.

$$x^{2}-8x+16-16=0$$

0 olish uchun 16 dan 16 ni ayirish.

$$x^{2}-8x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -8 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2}$$

\left(-8\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±8}{2}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±8}{2}$$

x=\frac{8±8}{2} tenglamasini yeching, bunda ± musbat. 8 ni 8 ga qo'shish.

$$x=\frac{16}{2}$$

16 ni 2 ga bo'lish.

$$x=8$$

x=\frac{8±8}{2} tenglamasini yeching, bunda ± manfiy. 8 dan 8 ni ayirish.

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

0 ni 2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=8 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{16}$$

Qisqartirish.

$$x-4=4 x-4=-4$$

4 ni tenglamaning ikkala tarafiga qo'shish.

$$x=8 x=0$$