2x*(x+1)+(x-2)*(2x-1/2)=(2x-1/2)^2-7/6x eching

$$2 x \cdot ( x + 1 ) + ( x - 2 ) \cdot ( 2 x - \frac { 1 } { 2 } ) = ( 2 x - \frac { 1 } { 2 } ) ^ { 2 } - \frac { 7 } { 6 } x$$

x uchun yechish

$$x = -\frac{9}{8} = -1\frac{1}{8} = -1,125$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$2x^{2}+2x+\left(x-2\right)\left(2x-\frac{1}{2}\right)=\left(2x-\frac{1}{2}\right)^{2}-\frac{7}{6}x$$

x-2 ga 2x-\frac{1}{2} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+2x+2x^{2}-\frac{9}{2}x+1=\left(2x-\frac{1}{2}\right)^{2}-\frac{7}{6}x$$

4x^{2} ni olish uchun 2x^{2} va 2x^{2} ni birlashtirish.

$$4x^{2}+2x-\frac{9}{2}x+1=\left(2x-\frac{1}{2}\right)^{2}-\frac{7}{6}x$$

-\frac{5}{2}x ni olish uchun 2x va -\frac{9}{2}x ni birlashtirish.

$$4x^{2}-\frac{5}{2}x+1=\left(2x-\frac{1}{2}\right)^{2}-\frac{7}{6}x$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(2x-\frac{1}{2}\right)^{2} kengaytirilishi uchun ishlating.

$$4x^{2}-\frac{5}{2}x+1=4x^{2}-2x+\frac{1}{4}-\frac{7}{6}x$$

-\frac{19}{6}x ni olish uchun -2x va -\frac{7}{6}x ni birlashtirish.

$$4x^{2}-\frac{5}{2}x+1=4x^{2}-\frac{19}{6}x+\frac{1}{4}$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$4x^{2}-\frac{5}{2}x+1-4x^{2}=-\frac{19}{6}x+\frac{1}{4}$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$-\frac{5}{2}x+1=-\frac{19}{6}x+\frac{1}{4}$$

\frac{19}{6}x ni ikki tarafga qo’shing.

$$-\frac{5}{2}x+1+\frac{19}{6}x=\frac{1}{4}$$

\frac{2}{3}x ni olish uchun -\frac{5}{2}x va \frac{19}{6}x ni birlashtirish.

$$\frac{2}{3}x+1=\frac{1}{4}$$

Ikkala tarafdan 1 ni ayirish.

$$\frac{2}{3}x=\frac{1}{4}-1$$

-\frac{3}{4} olish uchun \frac{1}{4} dan 1 ni ayirish.

$$\frac{2}{3}x=-\frac{3}{4}$$

Ikki tarafini \frac{3}{2} va teskari kasri \frac{2}{3} ga ko‘paytiring.

$$x=-\frac{3}{4}\times \frac{3}{2}$$

-\frac{9}{8} hosil qilish uchun -\frac{3}{4} va \frac{3}{2} ni ko'paytirish.

$$x=-\frac{9}{8}$$