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

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

x uchun yechish

$$x=\sqrt{5}\approx 2,236067977$$

$$x=-\sqrt{5}\approx -2,236067977$$

Kvadrat ildizini topish bo'yicha qadamlar

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

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

x^{2} ni ikki tarafga qo’shing.

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

Ikkala tarafdan 2x ni ayirish.

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

0 ni olish uchun 2x va -2x ni birlashtirish.

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

2 ni ikki tarafga qo’shing.

$$x^{2}=3+2$$

5 olish uchun 3 va 2'ni qo'shing.

$$x^{2}=5$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=\sqrt{5} x=-\sqrt{5}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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

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

x^{2} ni ikki tarafga qo’shing.

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

Ikkala tarafdan 2x ni ayirish.

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

0 ni olish uchun 2x va -2x ni birlashtirish.

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

Ikkala tarafdan 3 ni ayirish.

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

-5 olish uchun -2 dan 3 ni ayirish.

$$-5+x^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$x^{2}-5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, 0 ni b va -5 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)}}{2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\left(-5\right)}}{2}$$

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{20}}{2}$$

20 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{5}}{2}$$

x=\frac{0±2\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat.

$$x=\sqrt{5}$$

x=\frac{0±2\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy.

$$x=-\sqrt{5}$$

Tenglama yechildi.

$$x=\sqrt{5} x=-\sqrt{5}$$