2x^2+18=0 eching

$$2 x ^ { 2 } + 18 = 0$$

x uchun yechish (complex solution)

$$x=-3i$$

$$x=3i$$

Kvadrat ildizini topish bo'yicha qadamlar

Ikkala tarafdan 18 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$2x^{2}=-18$$

Ikki tarafini 2 ga bo‘ling.

$$x^{2}=\frac{-18}{2}$$

-9 ni olish uchun -18 ni 2 ga bo‘ling.

$$x^{2}=-9$$

Tenglama yechildi.

$$x=3i x=-3i$$

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.

$$2x^{2}+18=0$$

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 18 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 18}}{2\times 2}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 2\times 18}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-8\times 18}}{2\times 2}$$

-8 ni 18 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-144}}{2\times 2}$$

-144 ning kvadrat ildizini chiqarish.

$$x=\frac{0±12i}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{0±12i}{4}$$

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

$$x=3i$$

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

$$x=-3i$$

Tenglama yechildi.

$$x=3i x=-3i$$