2x^2+5=0 eching

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

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{10}i}{2}\approx -0-1,58113883i$$

$$x=\frac{\sqrt{10}i}{2}\approx 1,58113883i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 5 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=-\frac{5}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{10}i}{2} x=-\frac{\sqrt{10}i}{2}$$

Kvadrat tenglamalaridan foydalanish qoidalari

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.

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

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 5 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 5}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\times 5}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\times 5}}{2\times 2}$$

-8 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-40}}{2\times 2}$$

-40 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{10}i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{10}i}{4}$$

x=\frac{0±2\sqrt{10}i}{4} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{10}i}{2}$$

x=\frac{0±2\sqrt{10}i}{4} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{10}i}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{10}i}{2} x=-\frac{\sqrt{10}i}{2}$$