2a=-6a/a-4 eching

$$2 a = \frac { - 6 a } { a - 4 }$$

a uchun yechish

$$a=1$$

$$a=0$$

Faktorlash qadamlari

a qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini a-4 ga ko'paytirish.

$$2a\left(a-4\right)=-6a$$

2a ga a-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2a^{2}-8a=-6a$$

6a ni ikki tarafga qo’shing.

$$2a^{2}-8a+6a=0$$

-2a ni olish uchun -8a va 6a ni birlashtirish.

$$2a^{2}-2a=0$$

a omili.

$$a\left(2a-2\right)=0$$

Tenglamani yechish uchun a=0 va 2a-2=0 ni yeching.

$$a=0 a=1$$

Kvadrat tenglamalaridan foydalanish qoidalari

a qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini a-4 ga ko'paytirish.

$$2a\left(a-4\right)=-6a$$

2a ga a-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2a^{2}-8a=-6a$$

6a ni ikki tarafga qo’shing.

$$2a^{2}-8a+6a=0$$

-2a ni olish uchun -8a va 6a ni birlashtirish.

$$2a^{2}-2a=0$$

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

$$a=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}}}{2\times 2}$$

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

$$a=\frac{-\left(-2\right)±2}{2\times 2}$$

-2 ning teskarisi 2 ga teng.

$$a=\frac{2±2}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$a=\frac{2±2}{4}$$

a=\frac{2±2}{4} tenglamasini yeching, bunda ± musbat. 2 ni 2 ga qo'shish.

$$a=\frac{4}{4}$$

4 ni 4 ga bo'lish.

$$a=1$$

a=\frac{2±2}{4} tenglamasini yeching, bunda ± manfiy. 2 dan 2 ni ayirish.

$$a=\frac{0}{4}$$

0 ni 4 ga bo'lish.

$$a=0$$

Tenglama yechildi.

$$a=1 a=0$$

Kvadratni yakunlash bo'yicha qadamlar

a qiymati 4 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini a-4 ga ko'paytirish.

$$2a\left(a-4\right)=-6a$$

2a ga a-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2a^{2}-8a=-6a$$

6a ni ikki tarafga qo’shing.

$$2a^{2}-8a+6a=0$$

-2a ni olish uchun -8a va 6a ni birlashtirish.

$$2a^{2}-2a=0$$

Ikki tarafini 2 ga bo‘ling.

$$\frac{2a^{2}-2a}{2}=\frac{0}{2}$$

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

$$a^{2}+\left(-\frac{2}{2}\right)a=\frac{0}{2}$$

-2 ni 2 ga bo'lish.

$$a^{2}-a=\frac{0}{2}$$

0 ni 2 ga bo'lish.

$$a^{2}-a=0$$

-1 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{1}{2} olish uchun. Keyin, -\frac{1}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$a^{2}-a+\left(-\frac{1}{2}\right)^{2}=\left(-\frac{1}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{1}{2} kvadratini chiqarish.

$$a^{2}-a+\frac{1}{4}=\frac{1}{4}$$

a^{2}-a+\frac{1}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(a-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(a-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Qisqartirish.

$$a-\frac{1}{2}=\frac{1}{2} a-\frac{1}{2}=-\frac{1}{2}$$

\frac{1}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$a=1 a=0$$