x^2-2(1+3m)x+7(3+2m)=0 eching

$$x ^ { 2 } - 2 ( 1 + 3 m ) x + 7 ( 3 + 2 m ) = 0$$

m uchun yechish

$$m=-\frac{x^{2}-2x+21}{2\left(7-3x\right)}$$

$$x\neq \frac{7}{3}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

7 ga 3+2m ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-2\left(1+3m\right)x+21+14m=0$$

Ikkala tarafdan 21 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$x^{2}-2\left(1+3m\right)x+14m=-21$$

-2 ga 1+3m ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+\left(-2-6m\right)x+14m=-21$$

-2-6m ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-2x-6mx+14m=-21$$

Ikkala tarafdan x^{2} ni ayirish.

$$-2x-6mx+14m=-21-x^{2}$$

2x ni ikki tarafga qo’shing.

$$-6mx+14m=-21-x^{2}+2x$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-6x+14\right)m=-21-x^{2}+2x$$

Tenglama standart shaklda.

$$\left(14-6x\right)m=-x^{2}+2x-21$$

Ikki tarafini -6x+14 ga bo‘ling.

$$\frac{\left(14-6x\right)m}{14-6x}=\frac{-x^{2}+2x-21}{14-6x}$$

-6x+14 ga bo'lish -6x+14 ga ko'paytirishni bekor qiladi.

$$m=\frac{-x^{2}+2x-21}{14-6x}$$

-21-x^{2}+2x ni -6x+14 ga bo'lish.

$$m=\frac{-x^{2}+2x-21}{2\left(7-3x\right)}$$

x uchun yechish (complex solution)

$$x=\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1$$

$$x=-\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1$$

x uchun yechish

$$x=\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1$$

$$x=-\sqrt{\left(m-2\right)\left(9m+10\right)}+3m+1\text{, }m\leq -\frac{10}{9}\text{ or }m\geq 2$$