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

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

m uchun yechish

$$m=-\frac{4x}{1-2x}$$

$$x\neq \frac{1}{2}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2x^{2}+3x=2x^{2}+2xm-x-m$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}+2xm-x-m=2x^{2}+3x$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2xm-x-m=2x^{2}+3x-2x^{2}$$

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

$$2xm-x-m=3x$$

x ni ikki tarafga qo’shing.

$$2xm-m=3x+x$$

4x ni olish uchun 3x va x ni birlashtirish.

$$2xm-m=4x$$

m'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x-1\right)m=4x$$

Ikki tarafini 2x-1 ga bo‘ling.

$$\frac{\left(2x-1\right)m}{2x-1}=\frac{4x}{2x-1}$$

2x-1 ga bo'lish 2x-1 ga ko'paytirishni bekor qiladi.

$$m=\frac{4x}{2x-1}$$

x uchun yechish

$$x=-\frac{m}{2\left(2-m\right)}$$

$$m\neq 2$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2x^{2}+3x=2x^{2}+2xm-x-m$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2x^{2}+3x-2x^{2}=2xm-x-m$$

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

$$3x=2xm-x-m$$

Ikkala tarafdan 2xm ni ayirish.

$$3x-2xm=-x-m$$

x ni ikki tarafga qo’shing.

$$3x-2xm+x=-m$$

4x ni olish uchun 3x va x ni birlashtirish.

$$4x-2xm=-m$$

x'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(4-2m\right)x=-m$$

Ikki tarafini 4-2m ga bo‘ling.

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

4-2m ga bo'lish 4-2m ga ko'paytirishni bekor qiladi.

$$x=-\frac{m}{4-2m}$$

-m ni 4-2m ga bo'lish.

$$x=-\frac{m}{2\left(2-m\right)}$$