2x^2+10=0 eching

$$2 { x }^{ 2 } +10=0$$

x uchun yechish (complex solution)

$$x=-\sqrt{5}i\approx -0-2,236067977i$$

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

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 10 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$2x^{2}=-10$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{-10}{2}$$

-5 ni olish uchun -10 ni 2 ga bo‘ling.

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

Tenglama yechildi.

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

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.

$$2x^{2}+10=0$$

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 10 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 10}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\times 10}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\times 10}}{2\times 2}$$

-8 ni 10 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-80}}{2\times 2}$$

-80 ning kvadrat ildizini chiqarish.

$$x=\frac{0±4\sqrt{5}i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±4\sqrt{5}i}{4}$$

x=\frac{0±4\sqrt{5}i}{4} tenglamasini yeching, bunda ± musbat.

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

x=\frac{0±4\sqrt{5}i}{4} tenglamasini yeching, bunda ± manfiy.

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

Tenglama yechildi.

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