2(x^2-8)+5=25 eching

$$2 ( x ^ { 2 } - 8 ) + 5 = 25$$

x uchun yechish

$$x=3\sqrt{2}\approx 4,242640687$$

$$x=-3\sqrt{2}\approx -4,242640687$$

Kvadrat ildizini topish bo'yicha qadamlar

2 ga x^{2}-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}-16+5=25$$

-11 olish uchun -16 va 5'ni qo'shing.

$$2x^{2}-11=25$$

11 ni ikki tarafga qo’shing.

$$2x^{2}=25+11$$

36 olish uchun 25 va 11'ni qo'shing.

$$2x^{2}=36$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{36}{2}$$

18 ni olish uchun 36 ni 2 ga bo‘ling.

$$x^{2}=18$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$x=3\sqrt{2} x=-3\sqrt{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

2 ga x^{2}-8 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}-16+5=25$$

-11 olish uchun -16 va 5'ni qo'shing.

$$2x^{2}-11=25$$

Ikkala tarafdan 25 ni ayirish.

$$2x^{2}-11-25=0$$

-36 olish uchun -11 dan 25 ni ayirish.

$$2x^{2}-36=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 2 ni a, 0 ni b va -36 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-36\right)}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\left(-36\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\left(-36\right)}}{2\times 2}$$

-8 ni -36 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{288}}{2\times 2}$$

288 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12\sqrt{2}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±12\sqrt{2}}{4}$$

x=\frac{0±12\sqrt{2}}{4} tenglamasini yeching, bunda ± musbat.

$$x=3\sqrt{2}$$

x=\frac{0±12\sqrt{2}}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-3\sqrt{2}$$

Tenglama yechildi.

$$x=3\sqrt{2} x=-3\sqrt{2}$$