x^2-6x=0 eching

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

x uchun yechish

$$x=6$$

$$x=0$$

Faktorlash qadamlari

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

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

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

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

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

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

-6 ni bo‘lish, x shartining koeffitsienti, 2 ga -3 olish uchun. Keyin, -3 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-6x+\left(-3\right)^{2}=\left(-3\right)^{2}$$

-3 kvadratini chiqarish.

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

x^{2}-6x+9 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

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

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.

$$x=6 x=0$$