x^2=8x eching

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

x uchun yechish

$$x=8$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 8x 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

Ikkala tarafdan 8x 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

Ikkala tarafdan 8x ni ayirish.

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

-8 ni bo‘lish, x shartining koeffitsienti, 2 ga -4 olish uchun. Keyin, -4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-8x+\left(-4\right)^{2}=\left(-4\right)^{2}$$

-4 kvadratini chiqarish.

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

x^{2}-8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

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.

$$x=8 x=0$$