(-2-m)x^2-(3m+1)x+4=0 eching

$$( - 2 - m ) x ^ { 2 } - ( 3 m + 1 ) x + 4 = 0$$

m uchun yechish

$$m=\frac{4-x-2x^{2}}{x\left(x+3\right)}$$

$$x\neq -3\text{ and }x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

-2-m ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$-2x^{2}-mx^{2}-\left(3m+1\right)x+4=0$$

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

$$-2x^{2}-mx^{2}-\left(3mx+x\right)+4=0$$

3mx+x teskarisini topish uchun har birining teskarisini toping.

$$-2x^{2}-mx^{2}-3mx-x+4=0$$

2x^{2} ni ikki tarafga qo’shing. Har qanday songa nolni qo‘shsangiz, o‘zi chiqadi.

$$-mx^{2}-3mx-x+4=2x^{2}$$

x ni ikki tarafga qo’shing.

$$-mx^{2}-3mx+4=2x^{2}+x$$

Ikkala tarafdan 4 ni ayirish.

$$-mx^{2}-3mx=2x^{2}+x-4$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-x^{2}-3x\right)m=2x^{2}+x-4$$

Ikki tarafini -x^{2}-3x ga bo‘ling.

$$\frac{\left(-x^{2}-3x\right)m}{-x^{2}-3x}=\frac{2x^{2}+x-4}{-x^{2}-3x}$$

-x^{2}-3x ga bo'lish -x^{2}-3x ga ko'paytirishni bekor qiladi.

$$m=\frac{2x^{2}+x-4}{-x^{2}-3x}$$

2x^{2}+x-4 ni -x^{2}-3x ga bo'lish.

$$m=\frac{2x^{2}+x-4}{-x\left(x+3\right)}$$

x uchun yechish

$$\left\{\begin{matrix}x=-\frac{\sqrt{9m^{2}+22m+33}+3m+1}{2\left(m+2\right)}\text{; }x=-\frac{-\sqrt{9m^{2}+22m+33}+3m+1}{2\left(m+2\right)}\text{, }&m\neq -2\\x=-\frac{4}{5}\text{, }&m=-2\end{matrix}\right,$$