x^2-6x=2x^2+6x eching

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

x uchun yechish

$$x=-12$$

$$x=0$$

Faktorlash qadamlari

Ikkala tarafdan 2x^{2} ni ayirish.

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

-x^{2} ni olish uchun x^{2} va -2x^{2} ni birlashtirish.

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

Ikkala tarafdan 6x ni ayirish.

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

-12x ni olish uchun -6x va -6x ni birlashtirish.

$$-x^{2}-12x=0$$

x omili.

$$x\left(-x-12\right)=0$$

Tenglamani yechish uchun x=0 va -x-12=0 ni yeching.

$$x=0 x=-12$$

Kvadrat tenglamalaridan foydalanish qoidalari

Ikkala tarafdan 2x^{2} ni ayirish.

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

-x^{2} ni olish uchun x^{2} va -2x^{2} ni birlashtirish.

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

Ikkala tarafdan 6x ni ayirish.

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

-12x ni olish uchun -6x va -6x ni birlashtirish.

$$-x^{2}-12x=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -12 ni b va 0 ni c bilan almashtiring.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\left(-1\right)}$$

\left(-12\right)^{2} ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±12}{2\left(-1\right)}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±12}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{12±12}{-2}$$

x=\frac{12±12}{-2} tenglamasini yeching, bunda ± musbat. 12 ni 12 ga qo'shish.

$$x=\frac{24}{-2}$$

24 ni -2 ga bo'lish.

$$x=-12$$

x=\frac{12±12}{-2} tenglamasini yeching, bunda ± manfiy. 12 dan 12 ni ayirish.

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

0 ni -2 ga bo'lish.

$$x=0$$

Tenglama yechildi.

$$x=-12 x=0$$

Kvadratni yakunlash bo'yicha qadamlar

Ikkala tarafdan 2x^{2} ni ayirish.

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

-x^{2} ni olish uchun x^{2} va -2x^{2} ni birlashtirish.

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

Ikkala tarafdan 6x ni ayirish.

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

-12x ni olish uchun -6x va -6x ni birlashtirish.

$$-x^{2}-12x=0$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-12x}{-1}=\frac{0}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{12}{-1}\right)x=\frac{0}{-1}$$

-12 ni -1 ga bo'lish.

$$x^{2}+12x=\frac{0}{-1}$$

0 ni -1 ga bo'lish.

$$x^{2}+12x=0$$

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

$$x^{2}+12x+6^{2}=6^{2}$$

6 kvadratini chiqarish.

$$x^{2}+12x+36=36$$

x^{2}+12x+36 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+6\right)^{2}=36$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{36}$$

Qisqartirish.

$$x+6=6 x+6=-6$$

Tenglamaning ikkala tarafidan 6 ni ayirish.

$$x=0 x=-12$$