7x^2+5=0 eching

$$7 x ^ { 2 } + 5 = 0$$

x uchun yechish (complex solution)

$$x=-\frac{\sqrt{35}i}{7}\approx -0-0,845154255i$$

$$x=\frac{\sqrt{35}i}{7}\approx 0,845154255i$$

Kvadrat ildizini topish bo'yicha qadamlar

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

$$7x^{2}=-5$$

Ikki tarafini 7 ga bo‘ling.

$$x^{2}=-\frac{5}{7}$$

Tenglama yechildi.

$$x=\frac{\sqrt{35}i}{7} x=-\frac{\sqrt{35}i}{7}$$

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.

$$7x^{2}+5=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 7 ni a, 0 ni b va 5 ni c bilan almashtiring.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\times 5}}{2\times 7}$$

0 kvadratini chiqarish.

$$x=\frac{0±\sqrt{-4\times 7\times 5}}{2\times 7}$$

-4 ni 7 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-28\times 5}}{2\times 7}$$

-28 ni 5 marotabaga ko'paytirish.

$$x=\frac{0±\sqrt{-140}}{2\times 7}$$

-140 ning kvadrat ildizini chiqarish.

$$x=\frac{0±2\sqrt{35}i}{2\times 7}$$

2 ni 7 marotabaga ko'paytirish.

$$x=\frac{0±2\sqrt{35}i}{14}$$

x=\frac{0±2\sqrt{35}i}{14} tenglamasini yeching, bunda ± musbat.

$$x=\frac{\sqrt{35}i}{7}$$

x=\frac{0±2\sqrt{35}i}{14} tenglamasini yeching, bunda ± manfiy.

$$x=-\frac{\sqrt{35}i}{7}$$

Tenglama yechildi.

$$x=\frac{\sqrt{35}i}{7} x=-\frac{\sqrt{35}i}{7}$$